Math https://learnful.ca/ en Remix of Functions and Function Notation https://learnful.ca/lesson/801 <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--title--resource-tutorial.html.twig x field--node--title.html.twig * field--node--resource-tutorial.html.twig * field--title.html.twig * field--string.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'core/modules/node/templates/field--node--title.html.twig' --> <span>Remix of Functions and Function Notation</span> <!-- END OUTPUT from 'core/modules/node/templates/field--node--title.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--uid--resource-tutorial.html.twig x field--node--uid.html.twig * field--node--resource-tutorial.html.twig * field--uid.html.twig * field--entity-reference.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'core/modules/node/templates/field--node--uid.html.twig' --> <span> <!-- THEME DEBUG --> <!-- THEME HOOK: 'username' --> <!-- BEGIN OUTPUT from 'core/modules/user/templates/username.html.twig' --> <a title="View user profile." href="/member/ydahi" lang="" about="/member/ydahi" typeof="schema:Person" property="schema:name" datatype="">Yasin Dahi</a> <!-- END OUTPUT from 'core/modules/user/templates/username.html.twig' --> </span> <!-- END OUTPUT from 'core/modules/node/templates/field--node--uid.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--created--resource-tutorial.html.twig x field--node--created.html.twig * field--node--resource-tutorial.html.twig * field--created.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'core/modules/node/templates/field--node--created.html.twig' --> <span>Thu, 04/20/2023 - 13:43</span> <!-- END OUTPUT from 'core/modules/node/templates/field--node--created.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'links__node' --> <!-- FILE NAME SUGGESTIONS: * links--node.html.twig x links.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/system/links.html.twig' --> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/system/links.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-content-blocks--resource-tutorial.html.twig * field--node--field-content-blocks.html.twig * field--node--resource-tutorial.html.twig * field--field-content-blocks.html.twig * field--entity-reference-revisions.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-content-blocks field--type-entity-reference-revisions field--label-above"> <div class="field--label">Content Blocks</div> <div class="field--items"> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--paragraph--1400.html.twig * ds-1col--paragraph-basic-text-block-default.html.twig * ds-1col--paragraph-basic-text-block.html.twig * ds-1col--paragraph-default.html.twig * ds-1col--paragraph.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div class="paragraph paragraph--type-basic-text-block paragraph--view-mode-default ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--expert--paragraph--field-section-title--basic-text-block.html.twig * field--expert--paragraph--basic-text-block.html.twig * field--expert--paragraph--field-section-title.html.twig * field--expert--field-section-title--basic-text-block.html.twig * field--expert--basic-text-block.html.twig * field--expert--field-section-title.html.twig * field--expert.html.twig * field--ds-field-expert.html.twig * field--paragraph--field-section-title--basic-text-block.html.twig * field--paragraph--field-section-title.html.twig * field--paragraph--basic-text-block.html.twig * field--field-section-title.html.twig * field--string.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <h2 class="section-title" > Learning Objectives</h2> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--default--paragraph--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--default--paragraph--basic-text-block.html.twig * field--default--paragraph--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--default--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--default--basic-text-block.html.twig * field--default--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--default.html.twig * field--theme-ds-field-default.html.twig * field--paragraph--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--paragraph--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--paragraph--basic-text-block.html.twig * field--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--ds.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-dynamic-token-fieldparagraph-paragraph-text-block field--type-ds field--label-hidden field--item"><div class="p-textblock width-default" data-bgcolor="#FFFFFF"><div class="tex2jax_process"><p>In this section, you will:</p> <ul> <li>Determine whether a relation represents a function.</li> <li>Find the value of a function.</li> <li>Determine whether a function is one-to-one.</li> <li>Use the vertical line test to identify functions.</li> <li>Graph the functions listed in the library of functions.</li> </ul> <p>A jetliner changes altitude as its distance from the starting point of a flight increases. The weight of a growing child increases with time. In each case, one quantity depends on another. There is a relationship between the two quantities that we can describe, analyze, and use to make predictions. In this section, we will analyze such relationships.</p> </div></div></div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--paragraph--1401.html.twig * ds-1col--paragraph-basic-text-block-default.html.twig * ds-1col--paragraph-basic-text-block.html.twig * ds-1col--paragraph-default.html.twig * ds-1col--paragraph.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div class="paragraph paragraph--type-basic-text-block paragraph--view-mode-default ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--expert--paragraph--field-section-title--basic-text-block.html.twig * field--expert--paragraph--basic-text-block.html.twig * field--expert--paragraph--field-section-title.html.twig * field--expert--field-section-title--basic-text-block.html.twig * field--expert--basic-text-block.html.twig * field--expert--field-section-title.html.twig * field--expert.html.twig * field--ds-field-expert.html.twig * field--paragraph--field-section-title--basic-text-block.html.twig * field--paragraph--field-section-title.html.twig * field--paragraph--basic-text-block.html.twig * field--field-section-title.html.twig * field--string.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <h2 class="section-title" > Determining Whether a Relation Represents a Function</h2> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--default--paragraph--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--default--paragraph--basic-text-block.html.twig * field--default--paragraph--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--default--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--default--basic-text-block.html.twig * field--default--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--default.html.twig * field--theme-ds-field-default.html.twig * field--paragraph--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--paragraph--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--paragraph--basic-text-block.html.twig * field--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--ds.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-dynamic-token-fieldparagraph-paragraph-text-block field--type-ds field--label-hidden field--item"><div class="p-textblock width-default" data-bgcolor="#FFFFFF"><div class="tex2jax_process"><p>A relation is a set of ordered pairs. The set consisting of the first components of each ordered pair is called the <strong>domain </strong>and the set consisting of the second components of each ordered pair is called the <strong>range</strong>. Consider the following set of ordered pairs. The first numbers in each pair are the first five natural numbers. The second number in each pair is twice that of the first.</p> <p>$$\{(1,\text{ }2),\text{ }(2,\text{ }4),\text{ }(3,\text{ }6),\text{ }(4,\text{ }8),\text{ }(5,\text{ }10)\}$$</p> <p>The domain is \(\{1,\text{ }2,\text{ }3,\text{ }4,\text{ }5\}\). The range is \(\{2,\text{ }4,\text{ }6,\text{ }8,\text{ }10\}\).</p> <p>Note that each value in the domain is also known as an <strong>input</strong> value, or independent variable, and is often labeled with the lowercase letter \(x\). Each value in the range is also known as an <strong>output</strong> value, or dependent variable, and is often labeled lowercase letter \(y\).</p> <p>A function \(f\) is a relation that assigns a single value in the range to each value in the domain<em>.</em> In other words, no <em>x</em>-values are repeated. For our example that relates the first five natural numbers to numbers double their values, this relation is a function because each element in the domain, \(\{1, 2, 3, 4, 5\}\), is paired with exactly one element in the range, \(\{2, 4, 6, 8, 10\}\).</p> <p>Now let’s consider the set of ordered pairs that relates the terms “even” and “odd” to the first five natural numbers. It would appear as</p> <p>$$\{{(\text{odd},\text{ }1),\text{ }(\text{even},\text{ }2),\text{ }(\text{odd},\text{ }3),\text{ }(\text{even},\text{ }4),\text{ }(\text{odd},\text{ }5)}\}$$</p> <p>Notice that each element in the domain, \(\{even, odd\}\) is <em>not</em> paired with exactly one element in the range, \(\{1, 2, 3, 4, 5\}\). For example, the term “odd” corresponds to three values from the range, \(\{1, 3, 5\}\) and the term “even” corresponds to two values from the range, \(\{2, 4\}\). This violates the definition of a function, so this relation is not a function.</p> <p>Figure 1 compares relations that are functions and not functions.</p> </div></div></div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--paragraph--1402.html.twig * ds-1col--paragraph-image-with-caption-default.html.twig * ds-1col--paragraph-image-with-caption.html.twig * ds-1col--paragraph-default.html.twig * ds-1col--paragraph.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div class="paragraph paragraph--type-image-with-caption paragraph--view-mode-default ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field_group_html_element' --> <!-- FILE NAME SUGGESTIONS: * field-group-html-element--paragraph--image-with-caption--group-p-imagecaption.html.twig * field-group-html-element--paragraph--image-with-caption--div.html.twig * field-group-html-element--paragraph--group-p-imagecaption.html.twig * field-group-html-element--paragraph--image-with-caption.html.twig * field-group-html-element--paragraph--div.html.twig * field-group-html-element--group-p-imagecaption.html.twig * field-group-html-element--image-with-caption.html.twig * field-group-html-element--paragraph.html.twig * field-group-html-element--div.html.twig x field-group-html-element.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/field_group/templates/field-group-html-element.html.twig' --> <div class="p-imagecaption width-default"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--expert--paragraph--field-image--image-with-caption.html.twig * field--expert--paragraph--image-with-caption.html.twig * field--expert--paragraph--field-image.html.twig * field--expert--field-image--image-with-caption.html.twig * field--expert--image-with-caption.html.twig * field--expert--field-image.html.twig * field--expert.html.twig * field--ds-field-expert.html.twig * field--paragraph--field-image--image-with-caption.html.twig * field--paragraph--field-image.html.twig * field--paragraph--image-with-caption.html.twig * field--field-image.html.twig * field--image.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <figure width="narrow"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'colorbox_formatter' --> <!-- BEGIN OUTPUT from 'modules/contrib/colorbox/templates/colorbox-formatter.html.twig' --> <a href="https://learnful.ca/sites/default/files/up/para/field-image/2020-07/78/d47bde493af93fa714bfc3dbe2a30008d2b7a5f0.jpeg" title="Figure 1 (a) This relationship is a function because each input is associated with a single output. Note that input  q  and  r  both give output  n.  (b) This relationship is also a function. In this case, each input is associated with a single output." data-colorbox-gallery="" class="colorbox" data-cbox-img-attrs="{&quot;alt&quot;:&quot;Three relations that demonstrate what constitute a function.&quot;}"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'image_style' --> <!-- BEGIN OUTPUT from 'core/modules/image/templates/image-style.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'image' --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/system/image.html.twig' --> <img src="/sites/default/files/styles/xxl/public/up/para/field-image/2020-07/78/d47bde493af93fa714bfc3dbe2a30008d2b7a5f0.jpeg?itok=14jOLkeR" width="1400" height="349" alt="Three relations that demonstrate what constitute a function." typeof="foaf:Image" class="img-responsive" /> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/system/image.html.twig' --> <!-- END OUTPUT from 'core/modules/image/templates/image-style.html.twig' --> </a> <!-- END OUTPUT from 'modules/contrib/colorbox/templates/colorbox-formatter.html.twig' --> </figure> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--expert--paragraph--field-image-caption--image-with-caption.html.twig * field--expert--paragraph--image-with-caption.html.twig * field--expert--paragraph--field-image-caption.html.twig * field--expert--field-image-caption--image-with-caption.html.twig * field--expert--image-with-caption.html.twig * field--expert--field-image-caption.html.twig * field--expert.html.twig * field--ds-field-expert.html.twig * field--paragraph--field-image-caption--image-with-caption.html.twig * field--paragraph--field-image-caption.html.twig * field--paragraph--image-with-caption.html.twig * field--field-image-caption.html.twig * field--text.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <figcaption width="narrow"> <div class="tex2jax_process"><p>Figure 1 (a) This relationship is a function because each input is associated with a single output. Note that input  q  and  r  both give output  n.  (b) This relationship is also a function. In this case, each input is associated with a single output.</p> </div> </figcaption> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/field_group/templates/field-group-html-element.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--paragraph--1403.html.twig * ds-1col--paragraph-basic-text-block-default.html.twig * ds-1col--paragraph-basic-text-block.html.twig * ds-1col--paragraph-default.html.twig * ds-1col--paragraph.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div class="paragraph paragraph--type-basic-text-block paragraph--view-mode-default ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--expert--paragraph--field-section-title--basic-text-block.html.twig * field--expert--paragraph--basic-text-block.html.twig * field--expert--paragraph--field-section-title.html.twig * field--expert--field-section-title--basic-text-block.html.twig * field--expert--basic-text-block.html.twig * field--expert--field-section-title.html.twig * field--expert.html.twig * field--ds-field-expert.html.twig * field--paragraph--field-section-title--basic-text-block.html.twig * field--paragraph--field-section-title.html.twig * field--paragraph--basic-text-block.html.twig * field--field-section-title.html.twig * field--string.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <h2 class="section-title" > Functions</h2> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--default--paragraph--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--default--paragraph--basic-text-block.html.twig * field--default--paragraph--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--default--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--default--basic-text-block.html.twig * field--default--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--default.html.twig * field--theme-ds-field-default.html.twig * field--paragraph--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--paragraph--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--paragraph--basic-text-block.html.twig * field--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--ds.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-dynamic-token-fieldparagraph-paragraph-text-block field--type-ds field--label-hidden field--item"><div class="p-textblock width-default" data-bgcolor="#FFFFFF"><div class="tex2jax_process"><p>A <strong>function </strong>is a relation in which each possible input value leads to exactly one output value. We say “the output is a function of the input.”</p> <p>The input values make up the <strong>domain</strong>, and the output values make up the <strong>range</strong>.</p> </div></div></div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--paragraph--1404.html.twig * ds-1col--paragraph-basic-text-block-default.html.twig * ds-1col--paragraph-basic-text-block.html.twig * ds-1col--paragraph-default.html.twig * ds-1col--paragraph.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div class="paragraph paragraph--type-basic-text-block paragraph--view-mode-default ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--default--paragraph--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--default--paragraph--basic-text-block.html.twig * field--default--paragraph--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--default--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--default--basic-text-block.html.twig * field--default--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--default.html.twig * field--theme-ds-field-default.html.twig * field--paragraph--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--paragraph--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--paragraph--basic-text-block.html.twig * field--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--ds.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-dynamic-token-fieldparagraph-paragraph-text-block field--type-ds field--label-hidden field--item"><div class="p-textblock width-default" data-bgcolor="#FFFFFF"><div class="tex2jax_process"><h3>Examples</h3> <p>Given a relationship between two quantities, determine whether the relationship is a function.</p> </div></div></div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--paragraph--1405.html.twig * ds-1col--paragraph-interactive-content-h5p--default.html.twig * ds-1col--paragraph-interactive-content-h5p-.html.twig * ds-1col--paragraph-default.html.twig * ds-1col--paragraph.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div class="paragraph paragraph--type-interactive-content-h5p- paragraph--view-mode-default ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--default--paragraph--field-interactive-content--interactive-content-h5p-.html.twig * field--default--paragraph--interactive-content-h5p-.html.twig * field--default--paragraph--field-interactive-content.html.twig * field--default--field-interactive-content--interactive-content-h5p-.html.twig * field--default--interactive-content-h5p-.html.twig * field--default--field-interactive-content.html.twig * field--default.html.twig * field--theme-ds-field-default.html.twig * field--paragraph--field-interactive-content--interactive-content-h5p-.html.twig * field--paragraph--field-interactive-content.html.twig * field--paragraph--interactive-content-h5p-.html.twig * field--field-interactive-content.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-interactive-content field--type-entity-reference field--label-hidden field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--node--144.html.twig * ds-1col--node-resource-h5p-teaser.html.twig * ds-1col--node-resource-h5p.html.twig * ds-1col--node-teaser.html.twig * ds-1col--node.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div data-history-node-id="144" class="node node--type-resource-h5p node--view-mode-teaser ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--default--node--field-h5p-content--resource-h5p.html.twig * field--default--node--resource-h5p.html.twig * field--default--node--field-h5p-content.html.twig * field--default--field-h5p-content--resource-h5p.html.twig * field--default--resource-h5p.html.twig * field--default--field-h5p-content.html.twig * field--default.html.twig * field--theme-ds-field-default.html.twig * field--node--field-h5p-content--resource-h5p.html.twig * field--node--field-h5p-content.html.twig * field--node--resource-h5p.html.twig * field--field-h5p-content.html.twig * field--h5p.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-h5p-content field--type-h5p field--label-hidden field--item"><div class="h5p-iframe-wrapper"><iframe enable-annotation id="h5p-iframe-23" class="h5p-iframe" data-content-id="23" frameborder="0" scrolling="no"></iframe></div></div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--paragraph--1406.html.twig * ds-1col--paragraph-basic-text-block-default.html.twig * ds-1col--paragraph-basic-text-block.html.twig * ds-1col--paragraph-default.html.twig * ds-1col--paragraph.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div class="paragraph paragraph--type-basic-text-block paragraph--view-mode-default ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--expert--paragraph--field-section-title--basic-text-block.html.twig * field--expert--paragraph--basic-text-block.html.twig * field--expert--paragraph--field-section-title.html.twig * field--expert--field-section-title--basic-text-block.html.twig * field--expert--basic-text-block.html.twig * field--expert--field-section-title.html.twig * field--expert.html.twig * field--ds-field-expert.html.twig * field--paragraph--field-section-title--basic-text-block.html.twig * field--paragraph--field-section-title.html.twig * field--paragraph--basic-text-block.html.twig * field--field-section-title.html.twig * field--string.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <h2 class="section-title" > Using Function Notation</h2> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--default--paragraph--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--default--paragraph--basic-text-block.html.twig * field--default--paragraph--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--default--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--default--basic-text-block.html.twig * field--default--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--default.html.twig * field--theme-ds-field-default.html.twig * field--paragraph--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--paragraph--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--paragraph--basic-text-block.html.twig * field--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--ds.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-dynamic-token-fieldparagraph-paragraph-text-block field--type-ds field--label-hidden field--item"><div class="p-textblock width-default" data-bgcolor="#FFFFFF"><div class="tex2jax_process"><p>Once we determine that a relationship is a function, we need to display and define the functional relationships so that we can understand and use them, and sometimes also so that we can program them into computers. There are various ways of representing functions. A standard function notation is one representation that facilitates working with functions.</p> <p>To represent “height is a function of age,” we start by identifying the descriptive variables \(h\) for height and \(a\) for age. The letters \(f\), \(g\), and \(h\) are often used to represent functions just as we use \(x, y\), and \(z\) to represent numbers and \(A, B\), and \(C\) to represent sets.</p> <p>$$ \begin{array}{lcccc}h\text{ is }f\text{ of }a&&&&\text{We name the function }f;\text{ height is a function of age}.\\h=f(a)&&&&\text{We use parentheses to indicate the function input}\text{. }\\f(a)&&&&\text{We name the function }f;\text{ the expression is read as “}f\text{ of }a\text{.”}\end{array} $$</p> <p>Remember, we can use any letter to name the function; the notation \(h(a)\) shows us that \(h\) depends on \(a\). The value a  a must be put into the function \(h\) to get a result. The parentheses indicate that age is input into the function; they do not indicate multiplication.</p> <p>We can also give an algebraic expression as the input to a function. For example \(f(a+b)\) means "first add <em>a</em> and <em>b</em>, and the result is the input for the function <em>f</em>." The operations must be performed in this order to obtain the correct result.</p> <h3>Function Notation</h3> <p>The notation \(y=f(x)\) defines a function named \(f\). This is read as "\(y is a function of x\)". The letter \(x\) represents the input value, or independent variable. The letter \(y\), or \(f(x)\), represents the output value, or dependent variable.</p> </div></div></div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--paragraph--1407.html.twig * ds-1col--paragraph-interactive-content-h5p--default.html.twig * ds-1col--paragraph-interactive-content-h5p-.html.twig * ds-1col--paragraph-default.html.twig * ds-1col--paragraph.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div class="paragraph paragraph--type-interactive-content-h5p- paragraph--view-mode-default ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--expert--paragraph--field-section-title--interactive-content-h5p-.html.twig * field--expert--paragraph--interactive-content-h5p-.html.twig * field--expert--paragraph--field-section-title.html.twig * field--expert--field-section-title--interactive-content-h5p-.html.twig * field--expert--interactive-content-h5p-.html.twig * field--expert--field-section-title.html.twig * field--expert.html.twig * field--ds-field-expert.html.twig * field--paragraph--field-section-title--interactive-content-h5p-.html.twig * field--paragraph--field-section-title.html.twig * field--paragraph--interactive-content-h5p-.html.twig * field--field-section-title.html.twig * field--string.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <h2 class="section-title" > Practice Quiz</h2> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--default--paragraph--field-interactive-content--interactive-content-h5p-.html.twig * field--default--paragraph--interactive-content-h5p-.html.twig * field--default--paragraph--field-interactive-content.html.twig * field--default--field-interactive-content--interactive-content-h5p-.html.twig * field--default--interactive-content-h5p-.html.twig * field--default--field-interactive-content.html.twig * field--default.html.twig * field--theme-ds-field-default.html.twig * field--paragraph--field-interactive-content--interactive-content-h5p-.html.twig * field--paragraph--field-interactive-content.html.twig * field--paragraph--interactive-content-h5p-.html.twig * field--field-interactive-content.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-interactive-content field--type-entity-reference field--label-hidden field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--node--145.html.twig * ds-1col--node-resource-h5p-teaser.html.twig * ds-1col--node-resource-h5p.html.twig * ds-1col--node-teaser.html.twig * ds-1col--node.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div data-history-node-id="145" class="node node--type-resource-h5p node--view-mode-teaser ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--default--node--field-h5p-content--resource-h5p.html.twig * field--default--node--resource-h5p.html.twig * field--default--node--field-h5p-content.html.twig * field--default--field-h5p-content--resource-h5p.html.twig * field--default--resource-h5p.html.twig * field--default--field-h5p-content.html.twig * field--default.html.twig * field--theme-ds-field-default.html.twig * field--node--field-h5p-content--resource-h5p.html.twig * field--node--field-h5p-content.html.twig * field--node--resource-h5p.html.twig * field--field-h5p-content.html.twig * field--h5p.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-h5p-content field--type-h5p field--label-hidden field--item"><div class="h5p-iframe-wrapper"><iframe enable-annotation id="h5p-iframe-24" class="h5p-iframe" data-content-id="24" frameborder="0" scrolling="no"></iframe></div></div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--paragraph--1409.html.twig * ds-1col--paragraph-notification-box-default.html.twig * ds-1col--paragraph-notification-box.html.twig * ds-1col--paragraph-default.html.twig * ds-1col--paragraph.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div class="paragraph paragraph--type-notification-box paragraph--view-mode-default ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--expert--paragraph--field-text-content--notification-box.html.twig * field--expert--paragraph--notification-box.html.twig * field--expert--paragraph--field-text-content.html.twig * field--expert--field-text-content--notification-box.html.twig * field--expert--notification-box.html.twig * field--expert--field-text-content.html.twig * field--expert.html.twig * field--ds-field-expert.html.twig * field--paragraph--field-text-content--notification-box.html.twig * field--paragraph--field-text-content.html.twig * field--paragraph--notification-box.html.twig * field--field-text-content.html.twig * field--text-long.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <div class="alert alert-info"> <p>Content for this page has been sourced from OpenStax - Access for free at https://openstax.org/books/algebra-and-trigonometry/pages/1-introduction-to-prerequisites</p> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> </div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-cover-image--resource-tutorial.html.twig * field--node--field-cover-image.html.twig * field--node--resource-tutorial.html.twig * field--field-cover-image.html.twig * field--image.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-cover-image field--type-image field--label-above"> <div class="field--label">Cover Image</div> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'image_formatter' --> <!-- BEGIN OUTPUT from 'core/modules/image/templates/image-formatter.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'image' --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/system/image.html.twig' --> <img src="/sites/default/files/up/tutorial/cover-image/2020-07/black-and-white-blur-book-business-240163.jpg" width="1280" height="720" alt="" typeof="foaf:Image" class="img-responsive" /> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/system/image.html.twig' --> <!-- END OUTPUT from 'core/modules/image/templates/image-formatter.html.twig' --> </div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-included-in-feeds--resource-tutorial.html.twig * field--node--field-included-in-feeds.html.twig * field--node--resource-tutorial.html.twig * field--field-included-in-feeds.html.twig * field--boolean.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-included-in-feeds field--type-boolean field--label-above"> <div class="field--label">Share in catalogue</div> <div class="field--item">Off</div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-tags--resource-tutorial.html.twig * field--node--field-tags.html.twig * field--node--resource-tutorial.html.twig * field--field-tags.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-tags field--type-entity-reference field--label-above"> <div class="field--label">Tags</div> <div class="field--items"> <div class="field--item"><a href="/taxonomy/term/166" hreflang="en">Math</a></div> <div class="field--item"><a href="/taxonomy/term/167" hreflang="en">Algebra</a></div> <div class="field--item"><a href="/taxonomy/term/168" hreflang="en">Functions</a></div> </div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-top-bar-region-tutorials--resource-tutorial.html.twig * field--node--field-top-bar-region-tutorials.html.twig * field--node--resource-tutorial.html.twig * field--field-top-bar-region-tutorials.html.twig * field--markup.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-top-bar-region-tutorials field--type-markup field--label-above"> <div class="field--label">Top Bar Region - Tutorials</div> <div class="field--item"><div class="col-md-6 hidden-xs hidden-sm" id="top-bar-left"> <div class="btn-group"> <a class="btn btn-primary btn-sm" href="/forum/3/creating-and-sharing-resources" target="_blank">Documentation</a> <!--<a class="btn btn-primary btn-sm" href="#">Help</a>--> </div> </div> <div class="col-md-6 text-right" id="top-bar-right"></div> </div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-creative-commons-license--resource-tutorial.html.twig * field--node--field-creative-commons-license.html.twig * field--node--resource-tutorial.html.twig * field--field-creative-commons-license.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-creative-commons-license field--type-entity-reference field--label-above"> <div class="field--label">Creative Commons License</div> <div class="field--item"><a href="/taxonomy/term/54" hreflang="en">CC BY</a></div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-education-level--resource-tutorial.html.twig * field--node--field-education-level.html.twig * field--node--resource-tutorial.html.twig * field--field-education-level.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-education-level field--type-entity-reference field--label-above"> <div class="field--label">Education Level</div> <div class="field--item"><a href="/taxonomy/term/134" hreflang="en">High School</a></div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-educational-use--resource-tutorial.html.twig * field--node--field-educational-use.html.twig * field--node--resource-tutorial.html.twig * field--field-educational-use.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-educational-use field--type-entity-reference field--label-above"> <div class="field--label">Educational Use</div> <div class="field--item"><a href="/taxonomy/term/109" hreflang="en">Instruction</a></div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-material-type--resource-tutorial.html.twig * field--node--field-material-type.html.twig * field--node--resource-tutorial.html.twig * field--field-material-type.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-material-type field--type-entity-reference field--label-above"> <div class="field--label">Material Type</div> <div class="field--item"><a href="/taxonomy/term/130" hreflang="en">Reading Material</a></div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-subject-area--resource-tutorial.html.twig * field--node--field-subject-area.html.twig * field--node--resource-tutorial.html.twig * field--field-subject-area.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-subject-area field--type-entity-reference field--label-above"> <div class="field--label">Subject Area</div> <div class="field--item"><a href="/taxonomy/term/149" hreflang="en">Mathematics</a></div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-brief-description--resource-tutorial.html.twig * field--node--field-brief-description.html.twig * field--node--resource-tutorial.html.twig * field--field-brief-description.html.twig * field--string-long.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-brief-description field--type-string-long field--label-above"> <div class="field--label">Brief Description</div> <div class="field--item">A demonstration of the MathJax authoring capabilities. Content for this page has been sourced from OpenStax - Access for free at https://openstax.org/books/algebra-and-trigonometry/pages/1-introduction-to-prerequisites</div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--comment--resource-tutorial.html.twig * field--node--comment.html.twig * field--node--resource-tutorial.html.twig x field--comment.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'themes/custom/learnful-theme/templates/field--comment.html.twig' --> <section id="node-resource-tutorial-comment"> <p class="for-guest"><a href="/login">Login</a> or <a href="/signup/beta">register</a> to join the discussion.</p> <div id="comment-list"> <h2>Comments</h2> <p class="text-muted small">Be the first to comment!</p> </div> </section> <!-- END OUTPUT from 'themes/custom/learnful-theme/templates/field--comment.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-report-adaption--resource-tutorial.html.twig * field--node--field-report-adaption.html.twig * field--node--resource-tutorial.html.twig x field--field-report-adaption.html.twig * field--comment.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'themes/custom/learnful-theme/templates/field--field-report-adaption.html.twig' --> <section id="node-resource-tutorial-field-report-adaption"> <p class="for-guest"><a href="/login">Login</a> or <a href="/signup/beta">register</a> to share your adaptations.</p> <div id="comment-list"> <h2>List of adaptions</h2> <p class="text-muted small">Be the first to add your adaptation here!</p> </div> </section> <!-- END OUTPUT from 'themes/custom/learnful-theme/templates/field--field-report-adaption.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-top-bar-region-lesson-clon--resource-tutorial.html.twig * field--node--field-top-bar-region-lesson-clon.html.twig * field--node--resource-tutorial.html.twig * field--field-top-bar-region-lesson-clon.html.twig * field--markup.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-top-bar-region-lesson-clon field--type-markup field--label-above"> <div class="field--label">Top Bar Region - Lesson - Clone</div> <div class="field--item"><div class="col-md-6 hidden-xs hidden-sm" id="top-bar-left"> <div class="btn-group"> </div> </div> <div class="col-md-6 text-right" id="top-bar-right"></div></div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-remix-of--resource-tutorial.html.twig * field--node--field-remix-of.html.twig * field--node--resource-tutorial.html.twig * field--field-remix-of.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-remix-of field--type-entity-reference field--label-above"> <div class="field--label">Remix of</div> <div class="field--item"><a href="/lesson/143" hreflang="en">Functions and Function Notation</a></div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-display-in-portfolio--resource-tutorial.html.twig * field--node--field-display-in-portfolio.html.twig * field--node--resource-tutorial.html.twig * field--field-display-in-portfolio.html.twig * field--boolean.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-display-in-portfolio field--type-boolean field--label-above"> <div class="field--label">Display in Portfolio</div> <div class="field--item">Off</div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-license-is-derivative--resource-tutorial.html.twig * field--node--field-license-is-derivative.html.twig * field--node--resource-tutorial.html.twig * field--field-license-is-derivative.html.twig * field--boolean.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-license-is-derivative field--type-boolean field--label-above"> <div class="field--label">This work is a derivative</div> <div class="field--item">Off</div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-feedback-review--resource-tutorial.html.twig * field--node--field-feedback-review.html.twig * field--node--resource-tutorial.html.twig x field--field-feedback-review.html.twig * field--comment.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'themes/custom/learnful-theme/templates/field--field-feedback-review.html.twig' --> <section id="node-resource-tutorial-field-feedback-review"> <p class="for-guest"><a href="/login">Login</a> or <a href="/signup/beta">register</a> to engage in the review and feedback process.</p> <div id="comment-list"> <h2>Reviews and Feedback</h2> <p class="text-muted small">Be the first to review!</p> </div> </section> <!-- END OUTPUT from 'themes/custom/learnful-theme/templates/field--field-feedback-review.html.twig' --> Thu, 20 Apr 2023 17:43:15 +0000 Yasin Dahi 801 at https://learnful.ca https://learnful.ca/lesson/801#comments https://learnful.ca/lesson/801#comments https://learnful.ca/lesson/801#comments 테스트 제목 - 21.11.05 https://learnful.ca/lesson/565 <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--title--resource-tutorial.html.twig x field--node--title.html.twig * field--node--resource-tutorial.html.twig * field--title.html.twig * field--string.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'core/modules/node/templates/field--node--title.html.twig' --> <span>테스트 제목 - 21.11.05</span> <!-- END OUTPUT from 'core/modules/node/templates/field--node--title.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--uid--resource-tutorial.html.twig x field--node--uid.html.twig * field--node--resource-tutorial.html.twig * field--uid.html.twig * field--entity-reference.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'core/modules/node/templates/field--node--uid.html.twig' --> <span> <!-- THEME DEBUG --> <!-- THEME HOOK: 'username' --> <!-- BEGIN OUTPUT from 'core/modules/user/templates/username.html.twig' --> <a title="View user profile." href="/member/choyunjin" lang="" about="/member/choyunjin" typeof="schema:Person" property="schema:name" datatype="">Yunjin Cho</a> <!-- END OUTPUT from 'core/modules/user/templates/username.html.twig' --> </span> <!-- END OUTPUT from 'core/modules/node/templates/field--node--uid.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--created--resource-tutorial.html.twig x field--node--created.html.twig * field--node--resource-tutorial.html.twig * field--created.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'core/modules/node/templates/field--node--created.html.twig' --> <span>Thu, 11/04/2021 - 19:25</span> <!-- END OUTPUT from 'core/modules/node/templates/field--node--created.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'links__node' --> <!-- FILE NAME SUGGESTIONS: * links--node.html.twig x links.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/system/links.html.twig' --> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/system/links.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-cover-image--resource-tutorial.html.twig * field--node--field-cover-image.html.twig * field--node--resource-tutorial.html.twig * field--field-cover-image.html.twig * field--image.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-cover-image field--type-image field--label-above"> <div class="field--label">Cover Image</div> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'image_formatter' --> <!-- BEGIN OUTPUT from 'core/modules/image/templates/image-formatter.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'image' --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/system/image.html.twig' --> <img src="/sites/default/files/up/tutorial/cover-image/2021-11/sunset.jpg" width="1920" height="1080" alt="" typeof="foaf:Image" class="img-responsive" /> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/system/image.html.twig' --> <!-- END OUTPUT from 'core/modules/image/templates/image-formatter.html.twig' --> </div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-included-in-feeds--resource-tutorial.html.twig * field--node--field-included-in-feeds.html.twig * field--node--resource-tutorial.html.twig * field--field-included-in-feeds.html.twig * field--boolean.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-included-in-feeds field--type-boolean field--label-above"> <div class="field--label">Share in catalogue</div> <div class="field--item">On</div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-tags--resource-tutorial.html.twig * field--node--field-tags.html.twig * field--node--resource-tutorial.html.twig * field--field-tags.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-tags field--type-entity-reference field--label-above"> <div class="field--label">Tags</div> <div class="field--items"> <div class="field--item"><a href="/taxonomy/term/166" hreflang="en">Math</a></div> </div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-top-bar-region-tutorials--resource-tutorial.html.twig * field--node--field-top-bar-region-tutorials.html.twig * field--node--resource-tutorial.html.twig * field--field-top-bar-region-tutorials.html.twig * field--markup.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-top-bar-region-tutorials field--type-markup field--label-above"> <div class="field--label">Top Bar Region - Tutorials</div> <div class="field--item"><div class="col-md-6 hidden-xs hidden-sm" id="top-bar-left"> <div class="btn-group"> <a class="btn btn-primary btn-sm" href="/forum/3/creating-and-sharing-resources" target="_blank">Documentation</a> <!--<a class="btn btn-primary btn-sm" href="#">Help</a>--> </div> </div> <div class="col-md-6 text-right" id="top-bar-right"></div> </div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-creative-commons-license--resource-tutorial.html.twig * field--node--field-creative-commons-license.html.twig * field--node--resource-tutorial.html.twig * field--field-creative-commons-license.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-creative-commons-license field--type-entity-reference field--label-above"> <div class="field--label">Creative Commons License</div> <div class="field--item"><a href="/taxonomy/term/55" hreflang="en">CC0</a></div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-brief-description--resource-tutorial.html.twig * field--node--field-brief-description.html.twig * field--node--resource-tutorial.html.twig * field--field-brief-description.html.twig * field--string-long.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-brief-description field--type-string-long field--label-above"> <div class="field--label">Brief Description</div> <div class="field--item">이것은 설명입니다. 설명 내 설명입니다. 내 설명 </div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--comment--resource-tutorial.html.twig * field--node--comment.html.twig * field--node--resource-tutorial.html.twig x field--comment.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'themes/custom/learnful-theme/templates/field--comment.html.twig' --> <section id="node-resource-tutorial-comment"> <p class="for-guest"><a href="/login">Login</a> or <a href="/signup/beta">register</a> to join the discussion.</p> <div id="comment-list"> <h2>Comments</h2> <p class="text-muted small">Be the first to comment!</p> </div> </section> <!-- END OUTPUT from 'themes/custom/learnful-theme/templates/field--comment.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-report-adaption--resource-tutorial.html.twig * field--node--field-report-adaption.html.twig * field--node--resource-tutorial.html.twig x field--field-report-adaption.html.twig * field--comment.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'themes/custom/learnful-theme/templates/field--field-report-adaption.html.twig' --> <section id="node-resource-tutorial-field-report-adaption"> <p class="for-guest"><a href="/login">Login</a> or <a href="/signup/beta">register</a> to share your adaptations.</p> <div id="comment-list"> <h2>List of adaptions</h2> <p class="text-muted small">Be the first to add your adaptation here!</p> </div> </section> <!-- END OUTPUT from 'themes/custom/learnful-theme/templates/field--field-report-adaption.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-top-bar-region-lesson-clon--resource-tutorial.html.twig * field--node--field-top-bar-region-lesson-clon.html.twig * field--node--resource-tutorial.html.twig * field--field-top-bar-region-lesson-clon.html.twig * field--markup.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-top-bar-region-lesson-clon field--type-markup field--label-above"> <div class="field--label">Top Bar Region - Lesson - Clone</div> <div class="field--item"><div class="col-md-6 hidden-xs hidden-sm" id="top-bar-left"> <div class="btn-group"> </div> </div> <div class="col-md-6 text-right" id="top-bar-right"></div></div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-display-in-portfolio--resource-tutorial.html.twig * field--node--field-display-in-portfolio.html.twig * field--node--resource-tutorial.html.twig * field--field-display-in-portfolio.html.twig * field--boolean.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-display-in-portfolio field--type-boolean field--label-above"> <div class="field--label">Display in Portfolio</div> <div class="field--item">On</div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-license-is-derivative--resource-tutorial.html.twig * field--node--field-license-is-derivative.html.twig * field--node--resource-tutorial.html.twig * field--field-license-is-derivative.html.twig * field--boolean.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-license-is-derivative field--type-boolean field--label-above"> <div class="field--label">This work is a derivative</div> <div class="field--item">Off</div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-feedback-review--resource-tutorial.html.twig * field--node--field-feedback-review.html.twig * field--node--resource-tutorial.html.twig x field--field-feedback-review.html.twig * field--comment.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'themes/custom/learnful-theme/templates/field--field-feedback-review.html.twig' --> <section id="node-resource-tutorial-field-feedback-review"> <p class="for-guest"><a href="/login">Login</a> or <a href="/signup/beta">register</a> to engage in the review and feedback process.</p> <div id="comment-list"> <h2>Reviews and Feedback</h2> <p class="text-muted small">Be the first to review!</p> </div> </section> <!-- END OUTPUT from 'themes/custom/learnful-theme/templates/field--field-feedback-review.html.twig' --> Thu, 04 Nov 2021 23:25:24 +0000 Yunjin Cho 565 at https://learnful.ca Remix of Functions and Function Notation https://learnful.ca/lesson/334 <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--title--resource-tutorial.html.twig x field--node--title.html.twig * field--node--resource-tutorial.html.twig * field--title.html.twig * field--string.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'core/modules/node/templates/field--node--title.html.twig' --> <span>Remix of Functions and Function Notation</span> <!-- END OUTPUT from 'core/modules/node/templates/field--node--title.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--uid--resource-tutorial.html.twig x field--node--uid.html.twig * field--node--resource-tutorial.html.twig * field--uid.html.twig * field--entity-reference.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'core/modules/node/templates/field--node--uid.html.twig' --> <span> <!-- THEME DEBUG --> <!-- THEME HOOK: 'username' --> <!-- BEGIN OUTPUT from 'core/modules/user/templates/username.html.twig' --> <a title="View user profile." href="/member/ydahi" lang="" about="/member/ydahi" typeof="schema:Person" property="schema:name" datatype="">Yasin Dahi</a> <!-- END OUTPUT from 'core/modules/user/templates/username.html.twig' --> </span> <!-- END OUTPUT from 'core/modules/node/templates/field--node--uid.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--created--resource-tutorial.html.twig x field--node--created.html.twig * field--node--resource-tutorial.html.twig * field--created.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'core/modules/node/templates/field--node--created.html.twig' --> <span>Tue, 12/08/2020 - 11:52</span> <!-- END OUTPUT from 'core/modules/node/templates/field--node--created.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'links__node' --> <!-- FILE NAME SUGGESTIONS: * links--node.html.twig x links.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/system/links.html.twig' --> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/system/links.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-content-blocks--resource-tutorial.html.twig * field--node--field-content-blocks.html.twig * field--node--resource-tutorial.html.twig * field--field-content-blocks.html.twig * field--entity-reference-revisions.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-content-blocks field--type-entity-reference-revisions field--label-above"> <div class="field--label">Content Blocks</div> <div class="field--items"> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--paragraph--852.html.twig * ds-1col--paragraph-basic-text-block-default.html.twig * ds-1col--paragraph-basic-text-block.html.twig * ds-1col--paragraph-default.html.twig * ds-1col--paragraph.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div class="paragraph paragraph--type-basic-text-block paragraph--view-mode-default ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--expert--paragraph--field-section-title--basic-text-block.html.twig * field--expert--paragraph--basic-text-block.html.twig * field--expert--paragraph--field-section-title.html.twig * field--expert--field-section-title--basic-text-block.html.twig * field--expert--basic-text-block.html.twig * field--expert--field-section-title.html.twig * field--expert.html.twig * field--ds-field-expert.html.twig * field--paragraph--field-section-title--basic-text-block.html.twig * field--paragraph--field-section-title.html.twig * field--paragraph--basic-text-block.html.twig * field--field-section-title.html.twig * field--string.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <h2 class="section-title" > Learning Objectives</h2> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--default--paragraph--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--default--paragraph--basic-text-block.html.twig * field--default--paragraph--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--default--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--default--basic-text-block.html.twig * field--default--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--default.html.twig * field--theme-ds-field-default.html.twig * field--paragraph--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--paragraph--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--paragraph--basic-text-block.html.twig * field--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--ds.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-dynamic-token-fieldparagraph-paragraph-text-block field--type-ds field--label-hidden field--item"><div class="p-textblock width-default" data-bgcolor="#FFFFFF"><div class="tex2jax_process"><p>In this section, you will:</p> <ul> <li>Determine whether a relation represents a function.</li> <li>Find the value of a function.</li> <li>Determine whether a function is one-to-one.</li> <li>Use the vertical line test to identify functions.</li> <li>Graph the functions listed in the library of functions.</li> </ul> <p>A jetliner changes altitude as its distance from the starting point of a flight increases. The weight of a growing child increases with time. In each case, one quantity depends on another. There is a relationship between the two quantities that we can describe, analyze, and use to make predictions. In this section, we will analyze such relationships.</p> </div></div></div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--paragraph--853.html.twig * ds-1col--paragraph-basic-text-block-default.html.twig * ds-1col--paragraph-basic-text-block.html.twig * ds-1col--paragraph-default.html.twig * ds-1col--paragraph.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div class="paragraph paragraph--type-basic-text-block paragraph--view-mode-default ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--expert--paragraph--field-section-title--basic-text-block.html.twig * field--expert--paragraph--basic-text-block.html.twig * field--expert--paragraph--field-section-title.html.twig * field--expert--field-section-title--basic-text-block.html.twig * field--expert--basic-text-block.html.twig * field--expert--field-section-title.html.twig * field--expert.html.twig * field--ds-field-expert.html.twig * field--paragraph--field-section-title--basic-text-block.html.twig * field--paragraph--field-section-title.html.twig * field--paragraph--basic-text-block.html.twig * field--field-section-title.html.twig * field--string.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <h2 class="section-title" > Determining Whether a Relation Represents a Function</h2> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--default--paragraph--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--default--paragraph--basic-text-block.html.twig * field--default--paragraph--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--default--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--default--basic-text-block.html.twig * field--default--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--default.html.twig * field--theme-ds-field-default.html.twig * field--paragraph--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--paragraph--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--paragraph--basic-text-block.html.twig * field--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--ds.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-dynamic-token-fieldparagraph-paragraph-text-block field--type-ds field--label-hidden field--item"><div class="p-textblock width-default" data-bgcolor="#FFFFFF"><div class="tex2jax_process"><p>A relation is a set of ordered pairs. The set consisting of the first components of each ordered pair is called the <strong>domain </strong>and the set consisting of the second components of each ordered pair is called the <strong>range</strong>. Consider the following set of ordered pairs. The first numbers in each pair are the first five natural numbers. The second number in each pair is twice that of the first.</p> <p>$$\{(1,\text{ }2),\text{ }(2,\text{ }4),\text{ }(3,\text{ }6),\text{ }(4,\text{ }8),\text{ }(5,\text{ }10)\}$$</p> <p>The domain is \(\{1,\text{ }2,\text{ }3,\text{ }4,\text{ }5\}\). The range is \(\{2,\text{ }4,\text{ }6,\text{ }8,\text{ }10\}\).</p> <p>Note that each value in the domain is also known as an <strong>input</strong> value, or independent variable, and is often labeled with the lowercase letter \(x\). Each value in the range is also known as an <strong>output</strong> value, or dependent variable, and is often labeled lowercase letter \(y\).</p> <p>A function \(f\) is a relation that assigns a single value in the range to each value in the domain<em>.</em> In other words, no <em>x</em>-values are repeated. For our example that relates the first five natural numbers to numbers double their values, this relation is a function because each element in the domain, \(\{1, 2, 3, 4, 5\}\), is paired with exactly one element in the range, \(\{2, 4, 6, 8, 10\}\).</p> <p>Now let’s consider the set of ordered pairs that relates the terms “even” and “odd” to the first five natural numbers. It would appear as</p> <p>$$\{{(\text{odd},\text{ }1),\text{ }(\text{even},\text{ }2),\text{ }(\text{odd},\text{ }3),\text{ }(\text{even},\text{ }4),\text{ }(\text{odd},\text{ }5)}\}$$</p> <p>Notice that each element in the domain, \(\{even, odd\}\) is <em>not</em> paired with exactly one element in the range, \(\{1, 2, 3, 4, 5\}\). For example, the term “odd” corresponds to three values from the range, \(\{1, 3, 5\}\) and the term “even” corresponds to two values from the range, \(\{2, 4\}\). This violates the definition of a function, so this relation is not a function.</p> <p>Figure 1 compares relations that are functions and not functions.</p> </div></div></div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--paragraph--854.html.twig * ds-1col--paragraph-image-with-caption-default.html.twig * ds-1col--paragraph-image-with-caption.html.twig * ds-1col--paragraph-default.html.twig * ds-1col--paragraph.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div class="paragraph paragraph--type-image-with-caption paragraph--view-mode-default ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field_group_html_element' --> <!-- FILE NAME SUGGESTIONS: * field-group-html-element--paragraph--image-with-caption--group-p-imagecaption.html.twig * field-group-html-element--paragraph--image-with-caption--div.html.twig * field-group-html-element--paragraph--group-p-imagecaption.html.twig * field-group-html-element--paragraph--image-with-caption.html.twig * field-group-html-element--paragraph--div.html.twig * field-group-html-element--group-p-imagecaption.html.twig * field-group-html-element--image-with-caption.html.twig * field-group-html-element--paragraph.html.twig * field-group-html-element--div.html.twig x field-group-html-element.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/field_group/templates/field-group-html-element.html.twig' --> <div class="p-imagecaption width-default"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--expert--paragraph--field-image--image-with-caption.html.twig * field--expert--paragraph--image-with-caption.html.twig * field--expert--paragraph--field-image.html.twig * field--expert--field-image--image-with-caption.html.twig * field--expert--image-with-caption.html.twig * field--expert--field-image.html.twig * field--expert.html.twig * field--ds-field-expert.html.twig * field--paragraph--field-image--image-with-caption.html.twig * field--paragraph--field-image.html.twig * field--paragraph--image-with-caption.html.twig * field--field-image.html.twig * field--image.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <figure width="narrow"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'colorbox_formatter' --> <!-- BEGIN OUTPUT from 'modules/contrib/colorbox/templates/colorbox-formatter.html.twig' --> <a href="https://learnful.ca/sites/default/files/up/para/field-image/2020-07/78/d47bde493af93fa714bfc3dbe2a30008d2b7a5f0.jpeg" title="Figure 1 (a) This relationship is a function because each input is associated with a single output. Note that input  q  and  r  both give output  n.  (b) This relationship is also a function. In this case, each input is associated with a single output." data-colorbox-gallery="" class="colorbox" data-cbox-img-attrs="{&quot;alt&quot;:&quot;Three relations that demonstrate what constitute a function.&quot;}"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'image_style' --> <!-- BEGIN OUTPUT from 'core/modules/image/templates/image-style.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'image' --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/system/image.html.twig' --> <img src="/sites/default/files/styles/xxl/public/up/para/field-image/2020-07/78/d47bde493af93fa714bfc3dbe2a30008d2b7a5f0.jpeg?itok=14jOLkeR" width="1400" height="349" alt="Three relations that demonstrate what constitute a function." typeof="foaf:Image" class="img-responsive" /> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/system/image.html.twig' --> <!-- END OUTPUT from 'core/modules/image/templates/image-style.html.twig' --> </a> <!-- END OUTPUT from 'modules/contrib/colorbox/templates/colorbox-formatter.html.twig' --> </figure> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--expert--paragraph--field-image-caption--image-with-caption.html.twig * field--expert--paragraph--image-with-caption.html.twig * field--expert--paragraph--field-image-caption.html.twig * field--expert--field-image-caption--image-with-caption.html.twig * field--expert--image-with-caption.html.twig * field--expert--field-image-caption.html.twig * field--expert.html.twig * field--ds-field-expert.html.twig * field--paragraph--field-image-caption--image-with-caption.html.twig * field--paragraph--field-image-caption.html.twig * field--paragraph--image-with-caption.html.twig * field--field-image-caption.html.twig * field--text.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <figcaption width="narrow"> <div class="tex2jax_process"><p>Figure 1 (a) This relationship is a function because each input is associated with a single output. Note that input  q  and  r  both give output  n.  (b) This relationship is also a function. In this case, each input is associated with a single output.</p> </div> </figcaption> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/field_group/templates/field-group-html-element.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--paragraph--855.html.twig * ds-1col--paragraph-basic-text-block-default.html.twig * ds-1col--paragraph-basic-text-block.html.twig * ds-1col--paragraph-default.html.twig * ds-1col--paragraph.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div class="paragraph paragraph--type-basic-text-block paragraph--view-mode-default ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--expert--paragraph--field-section-title--basic-text-block.html.twig * field--expert--paragraph--basic-text-block.html.twig * field--expert--paragraph--field-section-title.html.twig * field--expert--field-section-title--basic-text-block.html.twig * field--expert--basic-text-block.html.twig * field--expert--field-section-title.html.twig * field--expert.html.twig * field--ds-field-expert.html.twig * field--paragraph--field-section-title--basic-text-block.html.twig * field--paragraph--field-section-title.html.twig * field--paragraph--basic-text-block.html.twig * field--field-section-title.html.twig * field--string.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <h2 class="section-title" > Functions</h2> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--default--paragraph--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--default--paragraph--basic-text-block.html.twig * field--default--paragraph--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--default--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--default--basic-text-block.html.twig * field--default--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--default.html.twig * field--theme-ds-field-default.html.twig * field--paragraph--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--paragraph--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--paragraph--basic-text-block.html.twig * field--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--ds.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-dynamic-token-fieldparagraph-paragraph-text-block field--type-ds field--label-hidden field--item"><div class="p-textblock width-default" data-bgcolor="#FFFFFF"><div class="tex2jax_process"><p>A <strong>function </strong>is a relation in which each possible input value leads to exactly one output value. We say “the output is a function of the input.”</p> <p>The input values make up the <strong>domain</strong>, and the output values make up the <strong>range</strong>.</p> </div></div></div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--paragraph--856.html.twig * ds-1col--paragraph-basic-text-block-default.html.twig * ds-1col--paragraph-basic-text-block.html.twig * ds-1col--paragraph-default.html.twig * ds-1col--paragraph.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div class="paragraph paragraph--type-basic-text-block paragraph--view-mode-default ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--default--paragraph--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--default--paragraph--basic-text-block.html.twig * field--default--paragraph--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--default--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--default--basic-text-block.html.twig * field--default--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--default.html.twig * field--theme-ds-field-default.html.twig * field--paragraph--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--paragraph--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--paragraph--basic-text-block.html.twig * field--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--ds.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-dynamic-token-fieldparagraph-paragraph-text-block field--type-ds field--label-hidden field--item"><div class="p-textblock width-default" data-bgcolor="#FFFFFF"><div class="tex2jax_process"><h3>Examples</h3> <p>Given a relationship between two quantities, determine whether the relationship is a function.</p> </div></div></div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--paragraph--857.html.twig * ds-1col--paragraph-interactive-content-h5p--default.html.twig * ds-1col--paragraph-interactive-content-h5p-.html.twig * ds-1col--paragraph-default.html.twig * ds-1col--paragraph.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div class="paragraph paragraph--type-interactive-content-h5p- paragraph--view-mode-default ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--default--paragraph--field-interactive-content--interactive-content-h5p-.html.twig * field--default--paragraph--interactive-content-h5p-.html.twig * field--default--paragraph--field-interactive-content.html.twig * field--default--field-interactive-content--interactive-content-h5p-.html.twig * field--default--interactive-content-h5p-.html.twig * field--default--field-interactive-content.html.twig * field--default.html.twig * field--theme-ds-field-default.html.twig * field--paragraph--field-interactive-content--interactive-content-h5p-.html.twig * field--paragraph--field-interactive-content.html.twig * field--paragraph--interactive-content-h5p-.html.twig * field--field-interactive-content.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-interactive-content field--type-entity-reference field--label-hidden field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--node--144.html.twig * ds-1col--node-resource-h5p-teaser.html.twig * ds-1col--node-resource-h5p.html.twig * ds-1col--node-teaser.html.twig * ds-1col--node.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div data-history-node-id="144" class="node node--type-resource-h5p node--view-mode-teaser ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--default--node--field-h5p-content--resource-h5p.html.twig * field--default--node--resource-h5p.html.twig * field--default--node--field-h5p-content.html.twig * field--default--field-h5p-content--resource-h5p.html.twig * field--default--resource-h5p.html.twig * field--default--field-h5p-content.html.twig * field--default.html.twig * field--theme-ds-field-default.html.twig * field--node--field-h5p-content--resource-h5p.html.twig * field--node--field-h5p-content.html.twig * field--node--resource-h5p.html.twig * field--field-h5p-content.html.twig * field--h5p.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-h5p-content field--type-h5p field--label-hidden field--item"><div class="h5p-iframe-wrapper"><iframe enable-annotation id="h5p-iframe-23" class="h5p-iframe" data-content-id="23" frameborder="0" scrolling="no"></iframe></div></div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--paragraph--858.html.twig * ds-1col--paragraph-basic-text-block-default.html.twig * ds-1col--paragraph-basic-text-block.html.twig * ds-1col--paragraph-default.html.twig * ds-1col--paragraph.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div class="paragraph paragraph--type-basic-text-block paragraph--view-mode-default ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--expert--paragraph--field-section-title--basic-text-block.html.twig * field--expert--paragraph--basic-text-block.html.twig * field--expert--paragraph--field-section-title.html.twig * field--expert--field-section-title--basic-text-block.html.twig * field--expert--basic-text-block.html.twig * field--expert--field-section-title.html.twig * field--expert.html.twig * field--ds-field-expert.html.twig * field--paragraph--field-section-title--basic-text-block.html.twig * field--paragraph--field-section-title.html.twig * field--paragraph--basic-text-block.html.twig * field--field-section-title.html.twig * field--string.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <h2 class="section-title" > Using Function Notation</h2> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--default--paragraph--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--default--paragraph--basic-text-block.html.twig * field--default--paragraph--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--default--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--default--basic-text-block.html.twig * field--default--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--default.html.twig * field--theme-ds-field-default.html.twig * field--paragraph--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--paragraph--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--paragraph--basic-text-block.html.twig * field--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--ds.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-dynamic-token-fieldparagraph-paragraph-text-block field--type-ds field--label-hidden field--item"><div class="p-textblock width-default" data-bgcolor="#FFFFFF"><div class="tex2jax_process"><p>Once we determine that a relationship is a function, we need to display and define the functional relationships so that we can understand and use them, and sometimes also so that we can program them into computers. There are various ways of representing functions. A standard function notation is one representation that facilitates working with functions.</p> <p>To represent “height is a function of age,” we start by identifying the descriptive variables \(h\) for height and \(a\) for age. The letters \(f\), \(g\), and \(h\) are often used to represent functions just as we use \(x, y\), and \(z\) to represent numbers and \(A, B\), and \(C\) to represent sets.</p> <p>$$ \begin{array}{lcccc}h\text{ is }f\text{ of }a&&&&\text{We name the function }f;\text{ height is a function of age}.\\h=f(a)&&&&\text{We use parentheses to indicate the function input}\text{. }\\f(a)&&&&\text{We name the function }f;\text{ the expression is read as “}f\text{ of }a\text{.”}\end{array} $$</p> <p>Remember, we can use any letter to name the function; the notation \(h(a)\) shows us that \(h\) depends on \(a\). The value a  a must be put into the function \(h\) to get a result. The parentheses indicate that age is input into the function; they do not indicate multiplication.</p> <p>We can also give an algebraic expression as the input to a function. For example \(f(a+b)\) means "first add <em>a</em> and <em>b</em>, and the result is the input for the function <em>f</em>." The operations must be performed in this order to obtain the correct result.</p> <h3>Function Notation</h3> <p>The notation \(y=f(x)\) defines a function named \(f\). This is read as "\(y is a function of x\)". The letter \(x\) represents the input value, or independent variable. The letter \(y\), or \(f(x)\), represents the output value, or dependent variable.</p> </div></div></div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--paragraph--859.html.twig * ds-1col--paragraph-interactive-content-h5p--default.html.twig * ds-1col--paragraph-interactive-content-h5p-.html.twig * ds-1col--paragraph-default.html.twig * ds-1col--paragraph.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div class="paragraph paragraph--type-interactive-content-h5p- paragraph--view-mode-default ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--expert--paragraph--field-section-title--interactive-content-h5p-.html.twig * field--expert--paragraph--interactive-content-h5p-.html.twig * field--expert--paragraph--field-section-title.html.twig * field--expert--field-section-title--interactive-content-h5p-.html.twig * field--expert--interactive-content-h5p-.html.twig * field--expert--field-section-title.html.twig * field--expert.html.twig * field--ds-field-expert.html.twig * field--paragraph--field-section-title--interactive-content-h5p-.html.twig * field--paragraph--field-section-title.html.twig * field--paragraph--interactive-content-h5p-.html.twig * field--field-section-title.html.twig * field--string.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <h2 class="section-title" > Practice Quiz</h2> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--default--paragraph--field-interactive-content--interactive-content-h5p-.html.twig * field--default--paragraph--interactive-content-h5p-.html.twig * field--default--paragraph--field-interactive-content.html.twig * field--default--field-interactive-content--interactive-content-h5p-.html.twig * field--default--interactive-content-h5p-.html.twig * field--default--field-interactive-content.html.twig * field--default.html.twig * field--theme-ds-field-default.html.twig * field--paragraph--field-interactive-content--interactive-content-h5p-.html.twig * field--paragraph--field-interactive-content.html.twig * field--paragraph--interactive-content-h5p-.html.twig * field--field-interactive-content.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-interactive-content field--type-entity-reference field--label-hidden field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--node--145.html.twig * ds-1col--node-resource-h5p-teaser.html.twig * ds-1col--node-resource-h5p.html.twig * ds-1col--node-teaser.html.twig * ds-1col--node.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div data-history-node-id="145" class="node node--type-resource-h5p node--view-mode-teaser ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--default--node--field-h5p-content--resource-h5p.html.twig * field--default--node--resource-h5p.html.twig * field--default--node--field-h5p-content.html.twig * field--default--field-h5p-content--resource-h5p.html.twig * field--default--resource-h5p.html.twig * field--default--field-h5p-content.html.twig * field--default.html.twig * field--theme-ds-field-default.html.twig * field--node--field-h5p-content--resource-h5p.html.twig * field--node--field-h5p-content.html.twig * field--node--resource-h5p.html.twig * field--field-h5p-content.html.twig * field--h5p.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-h5p-content field--type-h5p field--label-hidden field--item"><div class="h5p-iframe-wrapper"><iframe enable-annotation id="h5p-iframe-24" class="h5p-iframe" data-content-id="24" frameborder="0" scrolling="no"></iframe></div></div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--paragraph--860.html.twig * ds-1col--paragraph-embed-code-default.html.twig * ds-1col--paragraph-embed-code.html.twig * ds-1col--paragraph-default.html.twig * ds-1col--paragraph.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div class="paragraph paragraph--type-embed-code paragraph--view-mode-default ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--default--paragraph--field-embed-code--embed-code.html.twig * field--default--paragraph--embed-code.html.twig * field--default--paragraph--field-embed-code.html.twig * field--default--field-embed-code--embed-code.html.twig * field--default--embed-code.html.twig * field--default--field-embed-code.html.twig * field--default.html.twig * field--theme-ds-field-default.html.twig * field--paragraph--field-embed-code--embed-code.html.twig * field--paragraph--field-embed-code.html.twig * field--paragraph--embed-code.html.twig * field--field-embed-code.html.twig * field--text-long.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-embed-code field--type-text-long field--label-hidden field--item"><iframe src="https://www.geogebra.org/classic/gjencrn6?embed" width="800" height="600" allowfullscreen="" frameborder="0"></iframe></div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--paragraph--861.html.twig * ds-1col--paragraph-notification-box-default.html.twig * ds-1col--paragraph-notification-box.html.twig * ds-1col--paragraph-default.html.twig * ds-1col--paragraph.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div class="paragraph paragraph--type-notification-box paragraph--view-mode-default ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--expert--paragraph--field-text-content--notification-box.html.twig * field--expert--paragraph--notification-box.html.twig * field--expert--paragraph--field-text-content.html.twig * field--expert--field-text-content--notification-box.html.twig * field--expert--notification-box.html.twig * field--expert--field-text-content.html.twig * field--expert.html.twig * field--ds-field-expert.html.twig * field--paragraph--field-text-content--notification-box.html.twig * field--paragraph--field-text-content.html.twig * field--paragraph--notification-box.html.twig * field--field-text-content.html.twig * field--text-long.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <div class="alert alert-info"> <p>Content for this page has been sourced from OpenStax - Access for free at https://openstax.org/books/algebra-and-trigonometry/pages/1-introduction-to-prerequisites</p> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--paragraph--862.html.twig * ds-1col--paragraph-interactive-content-h5p--default.html.twig * ds-1col--paragraph-interactive-content-h5p-.html.twig * ds-1col--paragraph-default.html.twig * ds-1col--paragraph.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div class="paragraph paragraph--type-interactive-content-h5p- paragraph--view-mode-default ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--default--paragraph--field-interactive-content--interactive-content-h5p-.html.twig * field--default--paragraph--interactive-content-h5p-.html.twig * field--default--paragraph--field-interactive-content.html.twig * field--default--field-interactive-content--interactive-content-h5p-.html.twig * field--default--interactive-content-h5p-.html.twig * field--default--field-interactive-content.html.twig * field--default.html.twig * field--theme-ds-field-default.html.twig * field--paragraph--field-interactive-content--interactive-content-h5p-.html.twig * field--paragraph--field-interactive-content.html.twig * field--paragraph--interactive-content-h5p-.html.twig * field--field-interactive-content.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-interactive-content field--type-entity-reference field--label-hidden field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--node--128.html.twig * ds-1col--node-resource-h5p-teaser.html.twig * ds-1col--node-resource-h5p.html.twig * ds-1col--node-teaser.html.twig * ds-1col--node.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div data-history-node-id="128" class="node node--type-resource-h5p node--view-mode-teaser ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--default--node--field-h5p-content--resource-h5p.html.twig * field--default--node--resource-h5p.html.twig * field--default--node--field-h5p-content.html.twig * field--default--field-h5p-content--resource-h5p.html.twig * field--default--resource-h5p.html.twig * field--default--field-h5p-content.html.twig * field--default.html.twig * field--theme-ds-field-default.html.twig * field--node--field-h5p-content--resource-h5p.html.twig * field--node--field-h5p-content.html.twig * field--node--resource-h5p.html.twig * field--field-h5p-content.html.twig * field--h5p.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-h5p-content field--type-h5p field--label-hidden field--item"><div class="h5p-iframe-wrapper"><iframe enable-annotation id="h5p-iframe-18" class="h5p-iframe" data-content-id="18" frameborder="0" scrolling="no"></iframe></div></div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> </div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-cover-image--resource-tutorial.html.twig * field--node--field-cover-image.html.twig * field--node--resource-tutorial.html.twig * field--field-cover-image.html.twig * field--image.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-cover-image field--type-image field--label-above"> <div class="field--label">Cover Image</div> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'image_formatter' --> <!-- BEGIN OUTPUT from 'core/modules/image/templates/image-formatter.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'image' --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/system/image.html.twig' --> <img src="/sites/default/files/up/tutorial/cover-image/2020-07/black-and-white-blur-book-business-240163.jpg" width="1280" height="720" alt="" typeof="foaf:Image" class="img-responsive" /> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/system/image.html.twig' --> <!-- END OUTPUT from 'core/modules/image/templates/image-formatter.html.twig' --> </div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-included-in-feeds--resource-tutorial.html.twig * field--node--field-included-in-feeds.html.twig * field--node--resource-tutorial.html.twig * field--field-included-in-feeds.html.twig * field--boolean.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-included-in-feeds field--type-boolean field--label-above"> <div class="field--label">Share in catalogue</div> <div class="field--item">On</div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-tags--resource-tutorial.html.twig * field--node--field-tags.html.twig * field--node--resource-tutorial.html.twig * field--field-tags.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-tags field--type-entity-reference field--label-above"> <div class="field--label">Tags</div> <div class="field--items"> <div class="field--item"><a href="/taxonomy/term/166" hreflang="en">Math</a></div> <div class="field--item"><a href="/taxonomy/term/167" hreflang="en">Algebra</a></div> <div class="field--item"><a href="/taxonomy/term/168" hreflang="en">Functions</a></div> </div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-top-bar-region-tutorials--resource-tutorial.html.twig * field--node--field-top-bar-region-tutorials.html.twig * field--node--resource-tutorial.html.twig * field--field-top-bar-region-tutorials.html.twig * field--markup.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-top-bar-region-tutorials field--type-markup field--label-above"> <div class="field--label">Top Bar Region - Tutorials</div> <div class="field--item"><div class="col-md-6 hidden-xs hidden-sm" id="top-bar-left"> <div class="btn-group"> <a class="btn btn-primary btn-sm" href="/forum/3/creating-and-sharing-resources" target="_blank">Documentation</a> <!--<a class="btn btn-primary btn-sm" href="#">Help</a>--> </div> </div> <div class="col-md-6 text-right" id="top-bar-right"></div> </div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-creative-commons-license--resource-tutorial.html.twig * field--node--field-creative-commons-license.html.twig * field--node--resource-tutorial.html.twig * field--field-creative-commons-license.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-creative-commons-license field--type-entity-reference field--label-above"> <div class="field--label">Creative Commons License</div> <div class="field--item"><a href="/taxonomy/term/54" hreflang="en">CC BY</a></div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-education-level--resource-tutorial.html.twig * field--node--field-education-level.html.twig * field--node--resource-tutorial.html.twig * field--field-education-level.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-education-level field--type-entity-reference field--label-above"> <div class="field--label">Education Level</div> <div class="field--item"><a href="/taxonomy/term/134" hreflang="en">High School</a></div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-educational-use--resource-tutorial.html.twig * field--node--field-educational-use.html.twig * field--node--resource-tutorial.html.twig * field--field-educational-use.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-educational-use field--type-entity-reference field--label-above"> <div class="field--label">Educational Use</div> <div class="field--item"><a href="/taxonomy/term/109" hreflang="en">Instruction</a></div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-material-type--resource-tutorial.html.twig * field--node--field-material-type.html.twig * field--node--resource-tutorial.html.twig * field--field-material-type.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-material-type field--type-entity-reference field--label-above"> <div class="field--label">Material Type</div> <div class="field--item"><a href="/taxonomy/term/130" hreflang="en">Reading Material</a></div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-subject-area--resource-tutorial.html.twig * field--node--field-subject-area.html.twig * field--node--resource-tutorial.html.twig * field--field-subject-area.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-subject-area field--type-entity-reference field--label-above"> <div class="field--label">Subject Area</div> <div class="field--item"><a href="/taxonomy/term/149" hreflang="en">Mathematics</a></div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-brief-description--resource-tutorial.html.twig * field--node--field-brief-description.html.twig * field--node--resource-tutorial.html.twig * field--field-brief-description.html.twig * field--string-long.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-brief-description field--type-string-long field--label-above"> <div class="field--label">Brief Description</div> <div class="field--item">A demonstration of the MathJax authoring capabilities. Content for this page has been sourced from OpenStax - Access for free at https://openstax.org/books/algebra-and-trigonometry/pages/1-introduction-to-prerequisites</div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--comment--resource-tutorial.html.twig * field--node--comment.html.twig * field--node--resource-tutorial.html.twig x field--comment.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'themes/custom/learnful-theme/templates/field--comment.html.twig' --> <section id="node-resource-tutorial-comment--2"> <p class="for-guest"><a href="/login">Login</a> or <a href="/signup/beta">register</a> to join the discussion.</p> <div id="comment-list"> <h2>Comments</h2> <p class="text-muted small">Be the first to comment!</p> </div> </section> <!-- END OUTPUT from 'themes/custom/learnful-theme/templates/field--comment.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-report-adaption--resource-tutorial.html.twig * field--node--field-report-adaption.html.twig * field--node--resource-tutorial.html.twig x field--field-report-adaption.html.twig * field--comment.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'themes/custom/learnful-theme/templates/field--field-report-adaption.html.twig' --> <section id="node-resource-tutorial-field-report-adaption--2"> <p class="for-guest"><a href="/login">Login</a> or <a href="/signup/beta">register</a> to share your adaptations.</p> <div id="comment-list"> <h2>List of adaptions</h2> <p class="text-muted small">Be the first to add your adaptation here!</p> </div> </section> <!-- END OUTPUT from 'themes/custom/learnful-theme/templates/field--field-report-adaption.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-top-bar-region-lesson-clon--resource-tutorial.html.twig * field--node--field-top-bar-region-lesson-clon.html.twig * field--node--resource-tutorial.html.twig * field--field-top-bar-region-lesson-clon.html.twig * field--markup.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-top-bar-region-lesson-clon field--type-markup field--label-above"> <div class="field--label">Top Bar Region - Lesson - Clone</div> <div class="field--item"><div class="col-md-6 hidden-xs hidden-sm" id="top-bar-left"> <div class="btn-group"> </div> </div> <div class="col-md-6 text-right" id="top-bar-right"></div></div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-remix-of--resource-tutorial.html.twig * field--node--field-remix-of.html.twig * field--node--resource-tutorial.html.twig * field--field-remix-of.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-remix-of field--type-entity-reference field--label-above"> <div class="field--label">Remix of</div> <div class="field--item"><a href="/lesson/143" hreflang="en">Functions and Function Notation</a></div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-display-in-portfolio--resource-tutorial.html.twig * field--node--field-display-in-portfolio.html.twig * field--node--resource-tutorial.html.twig * field--field-display-in-portfolio.html.twig * field--boolean.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-display-in-portfolio field--type-boolean field--label-above"> <div class="field--label">Display in Portfolio</div> <div class="field--item">Off</div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-collaborators-er--resource-tutorial.html.twig * field--node--field-collaborators-er.html.twig * field--node--resource-tutorial.html.twig * field--field-collaborators-er.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-collaborators-er field--type-entity-reference field--label-above"> <div class="field--label">Collaborators</div> <div class="field--items"> <div class="field--item"><a href="/member/samanthastudent" hreflang="en">Samantha James</a></div> </div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-license-is-derivative--resource-tutorial.html.twig * field--node--field-license-is-derivative.html.twig * field--node--resource-tutorial.html.twig * field--field-license-is-derivative.html.twig * field--boolean.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-license-is-derivative field--type-boolean field--label-above"> <div class="field--label">This work is a derivative</div> <div class="field--item">Off</div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-feedback-review--resource-tutorial.html.twig * field--node--field-feedback-review.html.twig * field--node--resource-tutorial.html.twig x field--field-feedback-review.html.twig * field--comment.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'themes/custom/learnful-theme/templates/field--field-feedback-review.html.twig' --> <section id="node-resource-tutorial-field-feedback-review--2"> <p class="for-guest"><a href="/login">Login</a> or <a href="/signup/beta">register</a> to engage in the review and feedback process.</p> <div id="comment-list"> <h2>Reviews and Feedback</h2> <p class="text-muted small">Be the first to review!</p> </div> </section> <!-- END OUTPUT from 'themes/custom/learnful-theme/templates/field--field-feedback-review.html.twig' --> Tue, 08 Dec 2020 16:52:47 +0000 Yasin Dahi 334 at https://learnful.ca https://learnful.ca/lesson/334#comments https://learnful.ca/lesson/334#comments https://learnful.ca/lesson/334#comments My Remix of Functions and Function Notation https://learnful.ca/lesson/273 <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--title--resource-tutorial.html.twig x field--node--title.html.twig * field--node--resource-tutorial.html.twig * field--title.html.twig * field--string.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'core/modules/node/templates/field--node--title.html.twig' --> <span>My Remix of Functions and Function Notation</span> <!-- END OUTPUT from 'core/modules/node/templates/field--node--title.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--uid--resource-tutorial.html.twig x field--node--uid.html.twig * field--node--resource-tutorial.html.twig * field--uid.html.twig * field--entity-reference.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'core/modules/node/templates/field--node--uid.html.twig' --> <span> <!-- THEME DEBUG --> <!-- THEME HOOK: 'username' --> <!-- BEGIN OUTPUT from 'core/modules/user/templates/username.html.twig' --> <a title="View user profile." href="/member/samanthastudent" lang="" about="/member/samanthastudent" typeof="schema:Person" property="schema:name" datatype="">Samantha James</a> <!-- END OUTPUT from 'core/modules/user/templates/username.html.twig' --> </span> <!-- END OUTPUT from 'core/modules/node/templates/field--node--uid.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--created--resource-tutorial.html.twig x field--node--created.html.twig * field--node--resource-tutorial.html.twig * field--created.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'core/modules/node/templates/field--node--created.html.twig' --> <span>Thu, 11/12/2020 - 14:32</span> <!-- END OUTPUT from 'core/modules/node/templates/field--node--created.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'links__node' --> <!-- FILE NAME SUGGESTIONS: * links--node.html.twig x links.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/system/links.html.twig' --> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/system/links.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-content-blocks--resource-tutorial.html.twig * field--node--field-content-blocks.html.twig * field--node--resource-tutorial.html.twig * field--field-content-blocks.html.twig * field--entity-reference-revisions.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-content-blocks field--type-entity-reference-revisions field--label-above"> <div class="field--label">Content Blocks</div> <div class="field--items"> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--paragraph--687.html.twig * ds-1col--paragraph-basic-text-block-default.html.twig * ds-1col--paragraph-basic-text-block.html.twig * ds-1col--paragraph-default.html.twig * ds-1col--paragraph.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div class="paragraph paragraph--type-basic-text-block paragraph--view-mode-default ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--expert--paragraph--field-section-title--basic-text-block.html.twig * field--expert--paragraph--basic-text-block.html.twig * field--expert--paragraph--field-section-title.html.twig * field--expert--field-section-title--basic-text-block.html.twig * field--expert--basic-text-block.html.twig * field--expert--field-section-title.html.twig * field--expert.html.twig * field--ds-field-expert.html.twig * field--paragraph--field-section-title--basic-text-block.html.twig * field--paragraph--field-section-title.html.twig * field--paragraph--basic-text-block.html.twig * field--field-section-title.html.twig * field--string.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <h2 class="section-title" > Learning Objectives</h2> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--default--paragraph--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--default--paragraph--basic-text-block.html.twig * field--default--paragraph--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--default--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--default--basic-text-block.html.twig * field--default--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--default.html.twig * field--theme-ds-field-default.html.twig * field--paragraph--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--paragraph--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--paragraph--basic-text-block.html.twig * field--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--ds.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-dynamic-token-fieldparagraph-paragraph-text-block field--type-ds field--label-hidden field--item"><div class="p-textblock width-default" data-bgcolor="#FFFFFF"><div class="tex2jax_process"><p>In this section, you will:</p> <ul> <li>Determine whether a relation represents a function.</li> <li>Find the value of a function.</li> <li>Determine whether a function is one-to-one.</li> <li>Use the vertical line test to identify functions.</li> <li>Graph the functions listed in the library of functions.</li> </ul> <p>A jetliner changes altitude as its distance from the starting point of a flight increases. The weight of a growing child increases with time. In each case, one quantity depends on another. There is a relationship between the two quantities that we can describe, analyze, and use to make predictions. In this section, we will analyze such relationships.</p> </div></div></div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--paragraph--688.html.twig * ds-1col--paragraph-basic-text-block-default.html.twig * ds-1col--paragraph-basic-text-block.html.twig * ds-1col--paragraph-default.html.twig * ds-1col--paragraph.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div class="paragraph paragraph--type-basic-text-block paragraph--view-mode-default ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--expert--paragraph--field-section-title--basic-text-block.html.twig * field--expert--paragraph--basic-text-block.html.twig * field--expert--paragraph--field-section-title.html.twig * field--expert--field-section-title--basic-text-block.html.twig * field--expert--basic-text-block.html.twig * field--expert--field-section-title.html.twig * field--expert.html.twig * field--ds-field-expert.html.twig * field--paragraph--field-section-title--basic-text-block.html.twig * field--paragraph--field-section-title.html.twig * field--paragraph--basic-text-block.html.twig * field--field-section-title.html.twig * field--string.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <h2 class="section-title" > Determining Whether a Relation Represents a Function</h2> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--default--paragraph--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--default--paragraph--basic-text-block.html.twig * field--default--paragraph--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--default--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--default--basic-text-block.html.twig * field--default--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--default.html.twig * field--theme-ds-field-default.html.twig * field--paragraph--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--paragraph--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--paragraph--basic-text-block.html.twig * field--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--ds.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-dynamic-token-fieldparagraph-paragraph-text-block field--type-ds field--label-hidden field--item"><div class="p-textblock width-default" data-bgcolor="#FFFFFF"><div class="tex2jax_process"><p>A relation is a set of ordered pairs. The set consisting of the first components of each ordered pair is called the <strong>domain </strong>and the set consisting of the second components of each ordered pair is called the <strong>range</strong>. Consider the following set of ordered pairs. The first numbers in each pair are the first five natural numbers. The second number in each pair is twice that of the first.</p> <p>$$\{(1,\text{ }2),\text{ }(2,\text{ }4),\text{ }(3,\text{ }6),\text{ }(4,\text{ }8),\text{ }(5,\text{ }10)\}$$</p> <p>The domain is \(\{1,\text{ }2,\text{ }3,\text{ }4,\text{ }5\}\). The range is \(\{2,\text{ }4,\text{ }6,\text{ }8,\text{ }10\}\).</p> <p>Note that each value in the domain is also known as an <strong>input</strong> value, or independent variable, and is often labeled with the lowercase letter \(x\). Each value in the range is also known as an <strong>output</strong> value, or dependent variable, and is often labeled lowercase letter \(y\).</p> <p>A function \(f\) is a relation that assigns a single value in the range to each value in the domain<em>.</em> In other words, no <em>x</em>-values are repeated. For our example that relates the first five natural numbers to numbers double their values, this relation is a function because each element in the domain, \(\{1, 2, 3, 4, 5\}\), is paired with exactly one element in the range, \(\{2, 4, 6, 8, 10\}\).</p> <p>Now let’s consider the set of ordered pairs that relates the terms “even” and “odd” to the first five natural numbers. It would appear as</p> <p>$$\{{(\text{odd},\text{ }1),\text{ }(\text{even},\text{ }2),\text{ }(\text{odd},\text{ }3),\text{ }(\text{even},\text{ }4),\text{ }(\text{odd},\text{ }5)}\}$$</p> <p>Notice that each element in the domain, \(\{even, odd\}\) is <em>not</em> paired with exactly one element in the range, \(\{1, 2, 3, 4, 5\}\). For example, the term “odd” corresponds to three values from the range, \(\{1, 3, 5\}\) and the term “even” corresponds to two values from the range, \(\{2, 4\}\). This violates the definition of a function, so this relation is not a function.</p> <p>Figure 1 compares relations that are functions and not functions.</p> </div></div></div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--paragraph--689.html.twig * ds-1col--paragraph-image-with-caption-default.html.twig * ds-1col--paragraph-image-with-caption.html.twig * ds-1col--paragraph-default.html.twig * ds-1col--paragraph.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div class="paragraph paragraph--type-image-with-caption paragraph--view-mode-default ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field_group_html_element' --> <!-- FILE NAME SUGGESTIONS: * field-group-html-element--paragraph--image-with-caption--group-p-imagecaption.html.twig * field-group-html-element--paragraph--image-with-caption--div.html.twig * field-group-html-element--paragraph--group-p-imagecaption.html.twig * field-group-html-element--paragraph--image-with-caption.html.twig * field-group-html-element--paragraph--div.html.twig * field-group-html-element--group-p-imagecaption.html.twig * field-group-html-element--image-with-caption.html.twig * field-group-html-element--paragraph.html.twig * field-group-html-element--div.html.twig x field-group-html-element.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/field_group/templates/field-group-html-element.html.twig' --> <div class="p-imagecaption width-default"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--expert--paragraph--field-image--image-with-caption.html.twig * field--expert--paragraph--image-with-caption.html.twig * field--expert--paragraph--field-image.html.twig * field--expert--field-image--image-with-caption.html.twig * field--expert--image-with-caption.html.twig * field--expert--field-image.html.twig * field--expert.html.twig * field--ds-field-expert.html.twig * field--paragraph--field-image--image-with-caption.html.twig * field--paragraph--field-image.html.twig * field--paragraph--image-with-caption.html.twig * field--field-image.html.twig * field--image.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <figure width="narrow"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'colorbox_formatter' --> <!-- BEGIN OUTPUT from 'modules/contrib/colorbox/templates/colorbox-formatter.html.twig' --> <a href="https://learnful.ca/sites/default/files/up/para/field-image/2020-07/78/d47bde493af93fa714bfc3dbe2a30008d2b7a5f0.jpeg" title="Figure 1 (a) This relationship is a function because each input is associated with a single output. Note that input  q  and  r  both give output  n.  (b) This relationship is also a function. In this case, each input is associated with a single output." data-colorbox-gallery="" class="colorbox" data-cbox-img-attrs="{&quot;alt&quot;:&quot;Three relations that demonstrate what constitute a function.&quot;}"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'image_style' --> <!-- BEGIN OUTPUT from 'core/modules/image/templates/image-style.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'image' --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/system/image.html.twig' --> <img src="/sites/default/files/styles/xxl/public/up/para/field-image/2020-07/78/d47bde493af93fa714bfc3dbe2a30008d2b7a5f0.jpeg?itok=14jOLkeR" width="1400" height="349" alt="Three relations that demonstrate what constitute a function." typeof="foaf:Image" class="img-responsive" /> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/system/image.html.twig' --> <!-- END OUTPUT from 'core/modules/image/templates/image-style.html.twig' --> </a> <!-- END OUTPUT from 'modules/contrib/colorbox/templates/colorbox-formatter.html.twig' --> </figure> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--expert--paragraph--field-image-caption--image-with-caption.html.twig * field--expert--paragraph--image-with-caption.html.twig * field--expert--paragraph--field-image-caption.html.twig * field--expert--field-image-caption--image-with-caption.html.twig * field--expert--image-with-caption.html.twig * field--expert--field-image-caption.html.twig * field--expert.html.twig * field--ds-field-expert.html.twig * field--paragraph--field-image-caption--image-with-caption.html.twig * field--paragraph--field-image-caption.html.twig * field--paragraph--image-with-caption.html.twig * field--field-image-caption.html.twig * field--text.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <figcaption width="narrow"> <div class="tex2jax_process"><p>Figure 1 (a) This relationship is a function because each input is associated with a single output. Note that input  q  and  r  both give output  n.  (b) This relationship is also a function. In this case, each input is associated with a single output.</p> </div> </figcaption> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/field_group/templates/field-group-html-element.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--paragraph--690.html.twig * ds-1col--paragraph-basic-text-block-default.html.twig * ds-1col--paragraph-basic-text-block.html.twig * ds-1col--paragraph-default.html.twig * ds-1col--paragraph.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div class="paragraph paragraph--type-basic-text-block paragraph--view-mode-default ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--expert--paragraph--field-section-title--basic-text-block.html.twig * field--expert--paragraph--basic-text-block.html.twig * field--expert--paragraph--field-section-title.html.twig * field--expert--field-section-title--basic-text-block.html.twig * field--expert--basic-text-block.html.twig * field--expert--field-section-title.html.twig * field--expert.html.twig * field--ds-field-expert.html.twig * field--paragraph--field-section-title--basic-text-block.html.twig * field--paragraph--field-section-title.html.twig * field--paragraph--basic-text-block.html.twig * field--field-section-title.html.twig * field--string.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <h2 class="section-title" > Functions</h2> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--default--paragraph--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--default--paragraph--basic-text-block.html.twig * field--default--paragraph--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--default--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--default--basic-text-block.html.twig * field--default--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--default.html.twig * field--theme-ds-field-default.html.twig * field--paragraph--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--paragraph--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--paragraph--basic-text-block.html.twig * field--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--ds.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-dynamic-token-fieldparagraph-paragraph-text-block field--type-ds field--label-hidden field--item"><div class="p-textblock width-default" data-bgcolor="#FFFFFF"><div class="tex2jax_process"><p>A <strong>function </strong>is a relation in which each possible input value leads to exactly one output value. We say “the output is a function of the input.”</p> <p>The input values make up the <strong>domain</strong>, and the output values make up the <strong>range</strong>.</p> </div></div></div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--paragraph--691.html.twig * ds-1col--paragraph-basic-text-block-default.html.twig * ds-1col--paragraph-basic-text-block.html.twig * ds-1col--paragraph-default.html.twig * ds-1col--paragraph.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div class="paragraph paragraph--type-basic-text-block paragraph--view-mode-default ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--default--paragraph--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--default--paragraph--basic-text-block.html.twig * field--default--paragraph--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--default--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--default--basic-text-block.html.twig * field--default--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--default.html.twig * field--theme-ds-field-default.html.twig * field--paragraph--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--paragraph--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--paragraph--basic-text-block.html.twig * field--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--ds.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-dynamic-token-fieldparagraph-paragraph-text-block field--type-ds field--label-hidden field--item"><div class="p-textblock width-default" data-bgcolor="#FFFFFF"><div class="tex2jax_process"><h3>Examples</h3> <p>Given a relationship between two quantities, determine whether the relationship is a function.</p> </div></div></div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--paragraph--692.html.twig * ds-1col--paragraph-interactive-content-h5p--default.html.twig * ds-1col--paragraph-interactive-content-h5p-.html.twig * ds-1col--paragraph-default.html.twig * ds-1col--paragraph.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div class="paragraph paragraph--type-interactive-content-h5p- paragraph--view-mode-default ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--default--paragraph--field-interactive-content--interactive-content-h5p-.html.twig * field--default--paragraph--interactive-content-h5p-.html.twig * field--default--paragraph--field-interactive-content.html.twig * field--default--field-interactive-content--interactive-content-h5p-.html.twig * field--default--interactive-content-h5p-.html.twig * field--default--field-interactive-content.html.twig * field--default.html.twig * field--theme-ds-field-default.html.twig * field--paragraph--field-interactive-content--interactive-content-h5p-.html.twig * field--paragraph--field-interactive-content.html.twig * field--paragraph--interactive-content-h5p-.html.twig * field--field-interactive-content.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-interactive-content field--type-entity-reference field--label-hidden field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--node--144.html.twig * ds-1col--node-resource-h5p-teaser.html.twig * ds-1col--node-resource-h5p.html.twig * ds-1col--node-teaser.html.twig * ds-1col--node.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div data-history-node-id="144" class="node node--type-resource-h5p node--view-mode-teaser ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--default--node--field-h5p-content--resource-h5p.html.twig * field--default--node--resource-h5p.html.twig * field--default--node--field-h5p-content.html.twig * field--default--field-h5p-content--resource-h5p.html.twig * field--default--resource-h5p.html.twig * field--default--field-h5p-content.html.twig * field--default.html.twig * field--theme-ds-field-default.html.twig * field--node--field-h5p-content--resource-h5p.html.twig * field--node--field-h5p-content.html.twig * field--node--resource-h5p.html.twig * field--field-h5p-content.html.twig * field--h5p.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-h5p-content field--type-h5p field--label-hidden field--item"><div class="h5p-iframe-wrapper"><iframe enable-annotation id="h5p-iframe-23" class="h5p-iframe" data-content-id="23" frameborder="0" scrolling="no"></iframe></div></div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--paragraph--693.html.twig * ds-1col--paragraph-basic-text-block-default.html.twig * ds-1col--paragraph-basic-text-block.html.twig * ds-1col--paragraph-default.html.twig * ds-1col--paragraph.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div class="paragraph paragraph--type-basic-text-block paragraph--view-mode-default ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--expert--paragraph--field-section-title--basic-text-block.html.twig * field--expert--paragraph--basic-text-block.html.twig * field--expert--paragraph--field-section-title.html.twig * field--expert--field-section-title--basic-text-block.html.twig * field--expert--basic-text-block.html.twig * field--expert--field-section-title.html.twig * field--expert.html.twig * field--ds-field-expert.html.twig * field--paragraph--field-section-title--basic-text-block.html.twig * field--paragraph--field-section-title.html.twig * field--paragraph--basic-text-block.html.twig * field--field-section-title.html.twig * field--string.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <h2 class="section-title" > Using Function Notation</h2> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--default--paragraph--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--default--paragraph--basic-text-block.html.twig * field--default--paragraph--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--default--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--default--basic-text-block.html.twig * field--default--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--default.html.twig * field--theme-ds-field-default.html.twig * field--paragraph--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--paragraph--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--paragraph--basic-text-block.html.twig * field--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--ds.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-dynamic-token-fieldparagraph-paragraph-text-block field--type-ds field--label-hidden field--item"><div class="p-textblock width-default" data-bgcolor="#FFFFFF"><div class="tex2jax_process"><p>Once we determine that a relationship is a function, we need to display and define the functional relationships so that we can understand and use them, and sometimes also so that we can program them into computers. There are various ways of representing functions. A standard function notation is one representation that facilitates working with functions.</p> <p>To represent “height is a function of age,” we start by identifying the descriptive variables \(h\) for height and \(a\) for age. The letters \(f\), \(g\), and \(h\) are often used to represent functions just as we use \(x, y\), and \(z\) to represent numbers and \(A, B\), and \(C\) to represent sets.</p> <p>$$ \begin{array}{lcccc}h\text{ is }f\text{ of }a&&&&\text{We name the function }f;\text{ height is a function of age}.\\h=f(a)&&&&\text{We use parentheses to indicate the function input}\text{. }\\f(a)&&&&\text{We name the function }f;\text{ the expression is read as “}f\text{ of }a\text{.”}\end{array} $$</p> <p>Remember, we can use any letter to name the function; the notation \(h(a)\) shows us that \(h\) depends on \(a\). The value a  a must be put into the function \(h\) to get a result. The parentheses indicate that age is input into the function; they do not indicate multiplication.</p> <p>We can also give an algebraic expression as the input to a function. For example \(f(a+b)\) means "first add <em>a</em> and <em>b</em>, and the result is the input for the function <em>f</em>." The operations must be performed in this order to obtain the correct result.</p> <h3>Function Notation</h3> <p>The notation \(y=f(x)\) defines a function named \(f\). This is read as "\(y is a function of x\)". The letter \(x\) represents the input value, or independent variable. The letter \(y\), or \(f(x)\), represents the output value, or dependent variable.</p> </div></div></div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--paragraph--694.html.twig * ds-1col--paragraph-interactive-content-h5p--default.html.twig * ds-1col--paragraph-interactive-content-h5p-.html.twig * ds-1col--paragraph-default.html.twig * ds-1col--paragraph.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div class="paragraph paragraph--type-interactive-content-h5p- paragraph--view-mode-default ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--expert--paragraph--field-section-title--interactive-content-h5p-.html.twig * field--expert--paragraph--interactive-content-h5p-.html.twig * field--expert--paragraph--field-section-title.html.twig * field--expert--field-section-title--interactive-content-h5p-.html.twig * field--expert--interactive-content-h5p-.html.twig * field--expert--field-section-title.html.twig * field--expert.html.twig * field--ds-field-expert.html.twig * field--paragraph--field-section-title--interactive-content-h5p-.html.twig * field--paragraph--field-section-title.html.twig * field--paragraph--interactive-content-h5p-.html.twig * field--field-section-title.html.twig * field--string.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <h2 class="section-title" > Practice Quiz</h2> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--default--paragraph--field-interactive-content--interactive-content-h5p-.html.twig * field--default--paragraph--interactive-content-h5p-.html.twig * field--default--paragraph--field-interactive-content.html.twig * field--default--field-interactive-content--interactive-content-h5p-.html.twig * field--default--interactive-content-h5p-.html.twig * field--default--field-interactive-content.html.twig * field--default.html.twig * field--theme-ds-field-default.html.twig * field--paragraph--field-interactive-content--interactive-content-h5p-.html.twig * field--paragraph--field-interactive-content.html.twig * field--paragraph--interactive-content-h5p-.html.twig * field--field-interactive-content.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-interactive-content field--type-entity-reference field--label-hidden field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--node--145.html.twig * ds-1col--node-resource-h5p-teaser.html.twig * ds-1col--node-resource-h5p.html.twig * ds-1col--node-teaser.html.twig * ds-1col--node.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div data-history-node-id="145" class="node node--type-resource-h5p node--view-mode-teaser ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--default--node--field-h5p-content--resource-h5p.html.twig * field--default--node--resource-h5p.html.twig * field--default--node--field-h5p-content.html.twig * field--default--field-h5p-content--resource-h5p.html.twig * field--default--resource-h5p.html.twig * field--default--field-h5p-content.html.twig * field--default.html.twig * field--theme-ds-field-default.html.twig * field--node--field-h5p-content--resource-h5p.html.twig * field--node--field-h5p-content.html.twig * field--node--resource-h5p.html.twig * field--field-h5p-content.html.twig * field--h5p.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-h5p-content field--type-h5p field--label-hidden field--item"><div class="h5p-iframe-wrapper"><iframe enable-annotation id="h5p-iframe-24" class="h5p-iframe" data-content-id="24" frameborder="0" scrolling="no"></iframe></div></div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--paragraph--695.html.twig * ds-1col--paragraph-embed-code-default.html.twig * ds-1col--paragraph-embed-code.html.twig * ds-1col--paragraph-default.html.twig * ds-1col--paragraph.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div class="paragraph paragraph--type-embed-code paragraph--view-mode-default ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--default--paragraph--field-embed-code--embed-code.html.twig * field--default--paragraph--embed-code.html.twig * field--default--paragraph--field-embed-code.html.twig * field--default--field-embed-code--embed-code.html.twig * field--default--embed-code.html.twig * field--default--field-embed-code.html.twig * field--default.html.twig * field--theme-ds-field-default.html.twig * field--paragraph--field-embed-code--embed-code.html.twig * field--paragraph--field-embed-code.html.twig * field--paragraph--embed-code.html.twig * field--field-embed-code.html.twig * field--text-long.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-embed-code field--type-text-long field--label-hidden field--item"><iframe src="https://www.geogebra.org/classic/gjencrn6?embed" width="800" height="600" allowfullscreen="" frameborder="0"></iframe></div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--paragraph--696.html.twig * ds-1col--paragraph-notification-box-default.html.twig * ds-1col--paragraph-notification-box.html.twig * ds-1col--paragraph-default.html.twig * ds-1col--paragraph.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div class="paragraph paragraph--type-notification-box paragraph--view-mode-default ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--expert--paragraph--field-text-content--notification-box.html.twig * field--expert--paragraph--notification-box.html.twig * field--expert--paragraph--field-text-content.html.twig * field--expert--field-text-content--notification-box.html.twig * field--expert--notification-box.html.twig * field--expert--field-text-content.html.twig * field--expert.html.twig * field--ds-field-expert.html.twig * field--paragraph--field-text-content--notification-box.html.twig * field--paragraph--field-text-content.html.twig * field--paragraph--notification-box.html.twig * field--field-text-content.html.twig * field--text-long.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <div class="alert alert-info"> <p>Content for this page has been sourced from OpenStax - Access for free at https://openstax.org/books/algebra-and-trigonometry/pages/1-introduction-to-prerequisites</p> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> </div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-cover-image--resource-tutorial.html.twig * field--node--field-cover-image.html.twig * field--node--resource-tutorial.html.twig * field--field-cover-image.html.twig * field--image.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-cover-image field--type-image field--label-above"> <div class="field--label">Cover Image</div> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'image_formatter' --> <!-- BEGIN OUTPUT from 'core/modules/image/templates/image-formatter.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'image' --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/system/image.html.twig' --> <img src="/sites/default/files/up/tutorial/cover-image/2020-07/black-and-white-blur-book-business-240163.jpg" width="1280" height="720" alt="" typeof="foaf:Image" class="img-responsive" /> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/system/image.html.twig' --> <!-- END OUTPUT from 'core/modules/image/templates/image-formatter.html.twig' --> </div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-included-in-feeds--resource-tutorial.html.twig * field--node--field-included-in-feeds.html.twig * field--node--resource-tutorial.html.twig * field--field-included-in-feeds.html.twig * field--boolean.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-included-in-feeds field--type-boolean field--label-above"> <div class="field--label">Share in catalogue</div> <div class="field--item">Off</div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-tags--resource-tutorial.html.twig * field--node--field-tags.html.twig * field--node--resource-tutorial.html.twig * field--field-tags.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-tags field--type-entity-reference field--label-above"> <div class="field--label">Tags</div> <div class="field--items"> <div class="field--item"><a href="/taxonomy/term/166" hreflang="en">Math</a></div> <div class="field--item"><a href="/taxonomy/term/167" hreflang="en">Algebra</a></div> <div class="field--item"><a href="/taxonomy/term/168" hreflang="en">Functions</a></div> </div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-top-bar-region-tutorials--resource-tutorial.html.twig * field--node--field-top-bar-region-tutorials.html.twig * field--node--resource-tutorial.html.twig * field--field-top-bar-region-tutorials.html.twig * field--markup.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-top-bar-region-tutorials field--type-markup field--label-above"> <div class="field--label">Top Bar Region - Tutorials</div> <div class="field--item"><div class="col-md-6 hidden-xs hidden-sm" id="top-bar-left"> <div class="btn-group"> <a class="btn btn-primary btn-sm" href="/forum/3/creating-and-sharing-resources" target="_blank">Documentation</a> <!--<a class="btn btn-primary btn-sm" href="#">Help</a>--> </div> </div> <div class="col-md-6 text-right" id="top-bar-right"></div> </div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-creative-commons-license--resource-tutorial.html.twig * field--node--field-creative-commons-license.html.twig * field--node--resource-tutorial.html.twig * field--field-creative-commons-license.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-creative-commons-license field--type-entity-reference field--label-above"> <div class="field--label">Creative Commons License</div> <div class="field--item"><a href="/taxonomy/term/54" hreflang="en">CC BY</a></div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-education-level--resource-tutorial.html.twig * field--node--field-education-level.html.twig * field--node--resource-tutorial.html.twig * field--field-education-level.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-education-level field--type-entity-reference field--label-above"> <div class="field--label">Education Level</div> <div class="field--item"><a href="/taxonomy/term/134" hreflang="en">High School</a></div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-educational-use--resource-tutorial.html.twig * field--node--field-educational-use.html.twig * field--node--resource-tutorial.html.twig * field--field-educational-use.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-educational-use field--type-entity-reference field--label-above"> <div class="field--label">Educational Use</div> <div class="field--item"><a href="/taxonomy/term/109" hreflang="en">Instruction</a></div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-material-type--resource-tutorial.html.twig * field--node--field-material-type.html.twig * field--node--resource-tutorial.html.twig * field--field-material-type.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-material-type field--type-entity-reference field--label-above"> <div class="field--label">Material Type</div> <div class="field--item"><a href="/taxonomy/term/130" hreflang="en">Reading Material</a></div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-subject-area--resource-tutorial.html.twig * field--node--field-subject-area.html.twig * field--node--resource-tutorial.html.twig * field--field-subject-area.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-subject-area field--type-entity-reference field--label-above"> <div class="field--label">Subject Area</div> <div class="field--item"><a href="/taxonomy/term/149" hreflang="en">Mathematics</a></div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-brief-description--resource-tutorial.html.twig * field--node--field-brief-description.html.twig * field--node--resource-tutorial.html.twig * field--field-brief-description.html.twig * field--string-long.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-brief-description field--type-string-long field--label-above"> <div class="field--label">Brief Description</div> <div class="field--item">A demonstration of the MathJax authoring capabilities. Content for this page has been sourced from OpenStax - Access for free at https://openstax.org/books/algebra-and-trigonometry/pages/1-introduction-to-prerequisites</div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--comment--resource-tutorial.html.twig * field--node--comment.html.twig * field--node--resource-tutorial.html.twig x field--comment.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'themes/custom/learnful-theme/templates/field--comment.html.twig' --> <section id="node-resource-tutorial-comment--3"> <p class="for-guest"><a href="/login">Login</a> or <a href="/signup/beta">register</a> to join the discussion.</p> <div id="comment-list"> <h2>Comments</h2> <p class="text-muted small">Be the first to comment!</p> </div> </section> <!-- END OUTPUT from 'themes/custom/learnful-theme/templates/field--comment.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-report-adaption--resource-tutorial.html.twig * field--node--field-report-adaption.html.twig * field--node--resource-tutorial.html.twig x field--field-report-adaption.html.twig * field--comment.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'themes/custom/learnful-theme/templates/field--field-report-adaption.html.twig' --> <section id="node-resource-tutorial-field-report-adaption--3"> <p class="for-guest"><a href="/login">Login</a> or <a href="/signup/beta">register</a> to share your adaptations.</p> <div id="comment-list"> <h2>List of adaptions</h2> <p class="text-muted small">Be the first to add your adaptation here!</p> </div> </section> <!-- END OUTPUT from 'themes/custom/learnful-theme/templates/field--field-report-adaption.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-top-bar-region-lesson-clon--resource-tutorial.html.twig * field--node--field-top-bar-region-lesson-clon.html.twig * field--node--resource-tutorial.html.twig * field--field-top-bar-region-lesson-clon.html.twig * field--markup.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-top-bar-region-lesson-clon field--type-markup field--label-above"> <div class="field--label">Top Bar Region - Lesson - Clone</div> <div class="field--item"><div class="col-md-6 hidden-xs hidden-sm" id="top-bar-left"> <div class="btn-group"> </div> </div> <div class="col-md-6 text-right" id="top-bar-right"></div></div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-remix-of--resource-tutorial.html.twig * field--node--field-remix-of.html.twig * field--node--resource-tutorial.html.twig * field--field-remix-of.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-remix-of field--type-entity-reference field--label-above"> <div class="field--label">Remix of</div> <div class="field--item"><a href="/lesson/143" hreflang="en">Functions and Function Notation</a></div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-display-in-portfolio--resource-tutorial.html.twig * field--node--field-display-in-portfolio.html.twig * field--node--resource-tutorial.html.twig * field--field-display-in-portfolio.html.twig * field--boolean.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-display-in-portfolio field--type-boolean field--label-above"> <div class="field--label">Display in Portfolio</div> <div class="field--item">On</div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-license-is-derivative--resource-tutorial.html.twig * field--node--field-license-is-derivative.html.twig * field--node--resource-tutorial.html.twig * field--field-license-is-derivative.html.twig * field--boolean.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-license-is-derivative field--type-boolean field--label-above"> <div class="field--label">This work is a derivative</div> <div class="field--item">Off</div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-feedback-review--resource-tutorial.html.twig * field--node--field-feedback-review.html.twig * field--node--resource-tutorial.html.twig x field--field-feedback-review.html.twig * field--comment.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'themes/custom/learnful-theme/templates/field--field-feedback-review.html.twig' --> <section id="node-resource-tutorial-field-feedback-review--3"> <p class="for-guest"><a href="/login">Login</a> or <a href="/signup/beta">register</a> to engage in the review and feedback process.</p> <div id="comment-list"> <h2>Reviews and Feedback</h2> <p class="text-muted small">Be the first to review!</p> </div> </section> <!-- END OUTPUT from 'themes/custom/learnful-theme/templates/field--field-feedback-review.html.twig' --> Thu, 12 Nov 2020 19:32:02 +0000 Samantha James 273 at https://learnful.ca https://learnful.ca/lesson/273#comments https://learnful.ca/lesson/273#comments https://learnful.ca/lesson/273#comments Remix of Functions and Function Notation https://learnful.ca/lesson/220 <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--title--resource-tutorial.html.twig x field--node--title.html.twig * field--node--resource-tutorial.html.twig * field--title.html.twig * field--string.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'core/modules/node/templates/field--node--title.html.twig' --> <span>Remix of Functions and Function Notation</span> <!-- END OUTPUT from 'core/modules/node/templates/field--node--title.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--uid--resource-tutorial.html.twig x field--node--uid.html.twig * field--node--resource-tutorial.html.twig * field--uid.html.twig * field--entity-reference.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'core/modules/node/templates/field--node--uid.html.twig' --> <span> <!-- THEME DEBUG --> <!-- THEME HOOK: 'username' --> <!-- BEGIN OUTPUT from 'core/modules/user/templates/username.html.twig' --> <a title="View user profile." href="/member/robinsheilds" lang="" about="/member/robinsheilds" typeof="schema:Person" property="schema:name" datatype="">Robin Shields</a> <!-- END OUTPUT from 'core/modules/user/templates/username.html.twig' --> </span> <!-- END OUTPUT from 'core/modules/node/templates/field--node--uid.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--created--resource-tutorial.html.twig x field--node--created.html.twig * field--node--resource-tutorial.html.twig * field--created.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'core/modules/node/templates/field--node--created.html.twig' --> <span>Fri, 08/14/2020 - 13:44</span> <!-- END OUTPUT from 'core/modules/node/templates/field--node--created.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'links__node' --> <!-- FILE NAME SUGGESTIONS: * links--node.html.twig x links.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/system/links.html.twig' --> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/system/links.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-content-blocks--resource-tutorial.html.twig * field--node--field-content-blocks.html.twig * field--node--resource-tutorial.html.twig * field--field-content-blocks.html.twig * field--entity-reference-revisions.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-content-blocks field--type-entity-reference-revisions field--label-above"> <div class="field--label">Content Blocks</div> <div class="field--items"> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--paragraph--558.html.twig * ds-1col--paragraph-basic-text-block-default.html.twig * ds-1col--paragraph-basic-text-block.html.twig * ds-1col--paragraph-default.html.twig * ds-1col--paragraph.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div class="paragraph paragraph--type-basic-text-block paragraph--view-mode-default ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--default--paragraph--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--default--paragraph--basic-text-block.html.twig * field--default--paragraph--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--default--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--default--basic-text-block.html.twig * field--default--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--default.html.twig * field--theme-ds-field-default.html.twig * field--paragraph--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--paragraph--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--paragraph--basic-text-block.html.twig * field--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--ds.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-dynamic-token-fieldparagraph-paragraph-text-block field--type-ds field--label-hidden field--item"><div class="p-textblock width-default" data-bgcolor="#FFFFFF"><div class="tex2jax_process"><h2>Learning Objectives</h2> <p>In this section, you will:</p> <ul> <li>Determine whether a relation represents a function.</li> <li>Find the value of a function.</li> <li>Determine whether a function is one-to-one.</li> <li>Use the vertical line test to identify functions.</li> <li>Graph the functions listed in the library of functions.</li> </ul> <p>A jetliner changes altitude as its distance from the starting point of a flight increases. The weight of a growing child increases with time. In each case, one quantity depends on another. There is a relationship between the two quantities that we can describe, analyze, and use to make predictions. In this section, we will analyze such relationships.</p> </div></div></div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--paragraph--559.html.twig * ds-1col--paragraph-basic-text-block-default.html.twig * ds-1col--paragraph-basic-text-block.html.twig * ds-1col--paragraph-default.html.twig * ds-1col--paragraph.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div class="paragraph paragraph--type-basic-text-block paragraph--view-mode-default ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--default--paragraph--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--default--paragraph--basic-text-block.html.twig * field--default--paragraph--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--default--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--default--basic-text-block.html.twig * field--default--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--default.html.twig * field--theme-ds-field-default.html.twig * field--paragraph--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--paragraph--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--paragraph--basic-text-block.html.twig * field--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--ds.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-dynamic-token-fieldparagraph-paragraph-text-block field--type-ds field--label-hidden field--item"><div class="p-textblock width-default" data-bgcolor="#FFFFFF"><div class="tex2jax_process"><h2>Determining Whether a Relation Represents a Function</h2> <p>A relation is a set of ordered pairs. The set consisting of the first components of each ordered pair is called the <strong>domain </strong>and the set consisting of the second components of each ordered pair is called the <strong>range</strong>. Consider the following set of ordered pairs. The first numbers in each pair are the first five natural numbers. The second number in each pair is twice that of the first.</p> <p>$$\{(1,\text{ }2),\text{ }(2,\text{ }4),\text{ }(3,\text{ }6),\text{ }(4,\text{ }8),\text{ }(5,\text{ }10)\}$$</p> <p>The domain is \(\{1,\text{ }2,\text{ }3,\text{ }4,\text{ }5\}\). The range is \(\{2,\text{ }4,\text{ }6,\text{ }8,\text{ }10\}\).</p> <p>Note that each value in the domain is also known as an <strong>input</strong> value, or independent variable, and is often labeled with the lowercase letter \(x\). Each value in the range is also known as an <strong>output</strong> value, or dependent variable, and is often labeled lowercase letter \(y\).</p> <p>A function \(f\) is a relation that assigns a single value in the range to each value in the domain<em>.</em> In other words, no <em>x</em>-values are repeated. For our example that relates the first five natural numbers to numbers double their values, this relation is a function because each element in the domain, \(\{1, 2, 3, 4, 5\}\), is paired with exactly one element in the range, \(\{2, 4, 6, 8, 10\}\).</p> <p>Now let’s consider the set of ordered pairs that relates the terms “even” and “odd” to the first five natural numbers. It would appear as</p> <p>$$\{{(\text{odd},\text{ }1),\text{ }(\text{even},\text{ }2),\text{ }(\text{odd},\text{ }3),\text{ }(\text{even},\text{ }4),\text{ }(\text{odd},\text{ }5)}\}$$</p> <p>Notice that each element in the domain, \(\{even, odd\}\) is <em>not</em> paired with exactly one element in the range, \(\{1, 2, 3, 4, 5\}\). For example, the term “odd” corresponds to three values from the range, \(\{1, 3, 5\}\) and the term “even” corresponds to two values from the range, \(\{2, 4\}\). This violates the definition of a function, so this relation is not a function.</p> <p>Figure 1 compares relations that are functions and not functions.</p> </div></div></div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--paragraph--560.html.twig * ds-1col--paragraph-image-with-caption-default.html.twig * ds-1col--paragraph-image-with-caption.html.twig * ds-1col--paragraph-default.html.twig * ds-1col--paragraph.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div class="paragraph paragraph--type-image-with-caption paragraph--view-mode-default ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field_group_html_element' --> <!-- FILE NAME SUGGESTIONS: * field-group-html-element--paragraph--image-with-caption--group-p-imagecaption.html.twig * field-group-html-element--paragraph--image-with-caption--div.html.twig * field-group-html-element--paragraph--group-p-imagecaption.html.twig * field-group-html-element--paragraph--image-with-caption.html.twig * field-group-html-element--paragraph--div.html.twig * field-group-html-element--group-p-imagecaption.html.twig * field-group-html-element--image-with-caption.html.twig * field-group-html-element--paragraph.html.twig * field-group-html-element--div.html.twig x field-group-html-element.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/field_group/templates/field-group-html-element.html.twig' --> <div class="p-imagecaption width-default"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--expert--paragraph--field-image--image-with-caption.html.twig * field--expert--paragraph--image-with-caption.html.twig * field--expert--paragraph--field-image.html.twig * field--expert--field-image--image-with-caption.html.twig * field--expert--image-with-caption.html.twig * field--expert--field-image.html.twig * field--expert.html.twig * field--ds-field-expert.html.twig * field--paragraph--field-image--image-with-caption.html.twig * field--paragraph--field-image.html.twig * field--paragraph--image-with-caption.html.twig * field--field-image.html.twig * field--image.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <figure width="narrow"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'colorbox_formatter' --> <!-- BEGIN OUTPUT from 'modules/contrib/colorbox/templates/colorbox-formatter.html.twig' --> <a href="https://learnful.ca/sites/default/files/up/para/field-image/2020-07/78/d47bde493af93fa714bfc3dbe2a30008d2b7a5f0.jpeg" title="Figure 1 (a) This relationship is a function because each input is associated with a single output. Note that input  q  and  r  both give output  n.  (b) This relationship is also a function. In this case, each input is associated with a single output." data-colorbox-gallery="" class="colorbox" data-cbox-img-attrs="{&quot;alt&quot;:&quot;Three relations that demonstrate what constitute a function.&quot;}"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'image_style' --> <!-- BEGIN OUTPUT from 'core/modules/image/templates/image-style.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'image' --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/system/image.html.twig' --> <img src="/sites/default/files/styles/xxl/public/up/para/field-image/2020-07/78/d47bde493af93fa714bfc3dbe2a30008d2b7a5f0.jpeg?itok=14jOLkeR" width="1400" height="349" alt="Three relations that demonstrate what constitute a function." typeof="foaf:Image" class="img-responsive" /> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/system/image.html.twig' --> <!-- END OUTPUT from 'core/modules/image/templates/image-style.html.twig' --> </a> <!-- END OUTPUT from 'modules/contrib/colorbox/templates/colorbox-formatter.html.twig' --> </figure> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--expert--paragraph--field-image-caption--image-with-caption.html.twig * field--expert--paragraph--image-with-caption.html.twig * field--expert--paragraph--field-image-caption.html.twig * field--expert--field-image-caption--image-with-caption.html.twig * field--expert--image-with-caption.html.twig * field--expert--field-image-caption.html.twig * field--expert.html.twig * field--ds-field-expert.html.twig * field--paragraph--field-image-caption--image-with-caption.html.twig * field--paragraph--field-image-caption.html.twig * field--paragraph--image-with-caption.html.twig * field--field-image-caption.html.twig * field--text.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <figcaption width="narrow"> <div class="tex2jax_process"><p>Figure 1 (a) This relationship is a function because each input is associated with a single output. Note that input  q  and  r  both give output  n.  (b) This relationship is also a function. In this case, each input is associated with a single output.</p> </div> </figcaption> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/field_group/templates/field-group-html-element.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--paragraph--561.html.twig * ds-1col--paragraph-basic-text-block-default.html.twig * ds-1col--paragraph-basic-text-block.html.twig * ds-1col--paragraph-default.html.twig * ds-1col--paragraph.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div class="paragraph paragraph--type-basic-text-block paragraph--view-mode-default ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--default--paragraph--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--default--paragraph--basic-text-block.html.twig * field--default--paragraph--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--default--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--default--basic-text-block.html.twig * field--default--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--default.html.twig * field--theme-ds-field-default.html.twig * field--paragraph--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--paragraph--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--paragraph--basic-text-block.html.twig * field--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--ds.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-dynamic-token-fieldparagraph-paragraph-text-block field--type-ds field--label-hidden field--item"><div class="p-textblock width-default" data-bgcolor="#FFFFFF"><div class="tex2jax_process"><h2>Functions</h2> <p>A <strong>function </strong>is a relation in which each possible input value leads to exactly one output value. We say “the output is a function of the input.”</p> <p>The input values make up the <strong>domain</strong>, and the output values make up the <strong>range</strong>.</p> </div></div></div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--paragraph--562.html.twig * ds-1col--paragraph-basic-text-block-default.html.twig * ds-1col--paragraph-basic-text-block.html.twig * ds-1col--paragraph-default.html.twig * ds-1col--paragraph.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div class="paragraph paragraph--type-basic-text-block paragraph--view-mode-default ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--default--paragraph--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--default--paragraph--basic-text-block.html.twig * field--default--paragraph--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--default--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--default--basic-text-block.html.twig * field--default--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--default.html.twig * field--theme-ds-field-default.html.twig * field--paragraph--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--paragraph--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--paragraph--basic-text-block.html.twig * field--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--ds.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-dynamic-token-fieldparagraph-paragraph-text-block field--type-ds field--label-hidden field--item"><div class="p-textblock width-default" data-bgcolor="#FFFFFF"><div class="tex2jax_process"><h3>Examples</h3> <p>Given a relationship between two quantities, determine whether the relationship is a function.</p> </div></div></div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--paragraph--563.html.twig * ds-1col--paragraph-interactive-content-h5p--default.html.twig * ds-1col--paragraph-interactive-content-h5p-.html.twig * ds-1col--paragraph-default.html.twig * ds-1col--paragraph.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div class="paragraph paragraph--type-interactive-content-h5p- paragraph--view-mode-default ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--default--paragraph--field-interactive-content--interactive-content-h5p-.html.twig * field--default--paragraph--interactive-content-h5p-.html.twig * field--default--paragraph--field-interactive-content.html.twig * field--default--field-interactive-content--interactive-content-h5p-.html.twig * field--default--interactive-content-h5p-.html.twig * field--default--field-interactive-content.html.twig * field--default.html.twig * field--theme-ds-field-default.html.twig * field--paragraph--field-interactive-content--interactive-content-h5p-.html.twig * field--paragraph--field-interactive-content.html.twig * field--paragraph--interactive-content-h5p-.html.twig * field--field-interactive-content.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-interactive-content field--type-entity-reference field--label-hidden field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--node--144.html.twig * ds-1col--node-resource-h5p-teaser.html.twig * ds-1col--node-resource-h5p.html.twig * ds-1col--node-teaser.html.twig * ds-1col--node.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div data-history-node-id="144" class="node node--type-resource-h5p node--view-mode-teaser ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--default--node--field-h5p-content--resource-h5p.html.twig * field--default--node--resource-h5p.html.twig * field--default--node--field-h5p-content.html.twig * field--default--field-h5p-content--resource-h5p.html.twig * field--default--resource-h5p.html.twig * field--default--field-h5p-content.html.twig * field--default.html.twig * field--theme-ds-field-default.html.twig * field--node--field-h5p-content--resource-h5p.html.twig * field--node--field-h5p-content.html.twig * field--node--resource-h5p.html.twig * field--field-h5p-content.html.twig * field--h5p.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-h5p-content field--type-h5p field--label-hidden field--item"><div class="h5p-iframe-wrapper"><iframe enable-annotation id="h5p-iframe-23" class="h5p-iframe" data-content-id="23" frameborder="0" scrolling="no"></iframe></div></div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--paragraph--564.html.twig * ds-1col--paragraph-basic-text-block-default.html.twig * ds-1col--paragraph-basic-text-block.html.twig * ds-1col--paragraph-default.html.twig * ds-1col--paragraph.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div class="paragraph paragraph--type-basic-text-block paragraph--view-mode-default ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--default--paragraph--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--default--paragraph--basic-text-block.html.twig * field--default--paragraph--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--default--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--default--basic-text-block.html.twig * field--default--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--default.html.twig * field--theme-ds-field-default.html.twig * field--paragraph--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--paragraph--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--paragraph--basic-text-block.html.twig * field--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--ds.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-dynamic-token-fieldparagraph-paragraph-text-block field--type-ds field--label-hidden field--item"><div class="p-textblock width-default" data-bgcolor="#FFFFFF"><div class="tex2jax_process"><h2>Using Function Notation</h2> <p>Once we determine that a relationship is a function, we need to display and define the functional relationships so that we can understand and use them, and sometimes also so that we can program them into computers. There are various ways of representing functions. A standard function notation is one representation that facilitates working with functions.</p> <p>To represent “height is a function of age,” we start by identifying the descriptive variables \(h\) for height and \(a\) for age. The letters \(f\), \(g\), and \(h\) are often used to represent functions just as we use \(x, y\), and \(z\) to represent numbers and \(A, B\), and \(C\) to represent sets.</p> <p>$$ \begin{array}{lcccc}h\text{ is }f\text{ of }a&&&&\text{We name the function }f;\text{ height is a function of age}.\\h=f(a)&&&&\text{We use parentheses to indicate the function input}\text{. }\\f(a)&&&&\text{We name the function }f;\text{ the expression is read as “}f\text{ of }a\text{.”}\end{array} $$</p> <p>Remember, we can use any letter to name the function; the notation \(h(a)\) shows us that \(h\) depends on \(a\). The value a  a must be put into the function \(h\) to get a result. The parentheses indicate that age is input into the function; they do not indicate multiplication.</p> <p>We can also give an algebraic expression as the input to a function. For example \(f(a+b)\) means "first add <em>a</em> and <em>b</em>, and the result is the input for the function <em>f</em>." The operations must be performed in this order to obtain the correct result.</p> <h3>Function Notation</h3> <p>The notation \(y=f(x)\) defines a function named \(f\). This is read as "\(y is a function of x\)". The letter \(x\) represents the input value, or independent variable. The letter \(y\), or \(f(x)\), represents the output value, or dependent variable.</p> </div></div></div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--paragraph--565.html.twig * ds-1col--paragraph-basic-text-block-default.html.twig * ds-1col--paragraph-basic-text-block.html.twig * ds-1col--paragraph-default.html.twig * ds-1col--paragraph.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div class="paragraph paragraph--type-basic-text-block paragraph--view-mode-default ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--default--paragraph--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--default--paragraph--basic-text-block.html.twig * field--default--paragraph--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--default--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--default--basic-text-block.html.twig * field--default--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--default.html.twig * field--theme-ds-field-default.html.twig * field--paragraph--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--paragraph--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--paragraph--basic-text-block.html.twig * field--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--ds.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-dynamic-token-fieldparagraph-paragraph-text-block field--type-ds field--label-hidden field--item"><div class="p-textblock width-default" data-bgcolor="#FFFFFF"><div class="tex2jax_process"><h2>Practice Quiz</h2> </div></div></div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--paragraph--566.html.twig * ds-1col--paragraph-interactive-content-h5p--default.html.twig * ds-1col--paragraph-interactive-content-h5p-.html.twig * ds-1col--paragraph-default.html.twig * ds-1col--paragraph.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div class="paragraph paragraph--type-interactive-content-h5p- paragraph--view-mode-default ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--default--paragraph--field-interactive-content--interactive-content-h5p-.html.twig * field--default--paragraph--interactive-content-h5p-.html.twig * field--default--paragraph--field-interactive-content.html.twig * field--default--field-interactive-content--interactive-content-h5p-.html.twig * field--default--interactive-content-h5p-.html.twig * field--default--field-interactive-content.html.twig * field--default.html.twig * field--theme-ds-field-default.html.twig * field--paragraph--field-interactive-content--interactive-content-h5p-.html.twig * field--paragraph--field-interactive-content.html.twig * field--paragraph--interactive-content-h5p-.html.twig * field--field-interactive-content.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-interactive-content field--type-entity-reference field--label-hidden field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--node--145.html.twig * ds-1col--node-resource-h5p-teaser.html.twig * ds-1col--node-resource-h5p.html.twig * ds-1col--node-teaser.html.twig * ds-1col--node.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div data-history-node-id="145" class="node node--type-resource-h5p node--view-mode-teaser ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--default--node--field-h5p-content--resource-h5p.html.twig * field--default--node--resource-h5p.html.twig * field--default--node--field-h5p-content.html.twig * field--default--field-h5p-content--resource-h5p.html.twig * field--default--resource-h5p.html.twig * field--default--field-h5p-content.html.twig * field--default.html.twig * field--theme-ds-field-default.html.twig * field--node--field-h5p-content--resource-h5p.html.twig * field--node--field-h5p-content.html.twig * field--node--resource-h5p.html.twig * field--field-h5p-content.html.twig * field--h5p.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-h5p-content field--type-h5p field--label-hidden field--item"><div class="h5p-iframe-wrapper"><iframe enable-annotation id="h5p-iframe-24" class="h5p-iframe" data-content-id="24" frameborder="0" scrolling="no"></iframe></div></div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--paragraph--567.html.twig * ds-1col--paragraph-basic-text-block-default.html.twig * ds-1col--paragraph-basic-text-block.html.twig * ds-1col--paragraph-default.html.twig * ds-1col--paragraph.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div class="paragraph paragraph--type-basic-text-block paragraph--view-mode-default ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--default--paragraph--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--default--paragraph--basic-text-block.html.twig * field--default--paragraph--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--default--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--default--basic-text-block.html.twig * field--default--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--default.html.twig * field--theme-ds-field-default.html.twig * field--paragraph--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--paragraph--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--paragraph--basic-text-block.html.twig * field--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--ds.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-dynamic-token-fieldparagraph-paragraph-text-block field--type-ds field--label-hidden field--item"><div class="p-textblock width-narrow" data-bgcolor="#DDDDDD"><div class="tex2jax_process"><p>Content for this page has been sourced from OpenStax - Access for free at <a href="https://openstax.org/books/algebra-and-trigonometry/pages/1-introduction-to-prerequisites">https://openstax.org/books/algebra-and-trigonometry/pages/1-introductio…</a></p> </div></div></div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--paragraph--568.html.twig * ds-1col--paragraph-embed-code-default.html.twig * ds-1col--paragraph-embed-code.html.twig * ds-1col--paragraph-default.html.twig * ds-1col--paragraph.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div class="paragraph paragraph--type-embed-code paragraph--view-mode-default ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--default--paragraph--field-embed-code--embed-code.html.twig * field--default--paragraph--embed-code.html.twig * field--default--paragraph--field-embed-code.html.twig * field--default--field-embed-code--embed-code.html.twig * field--default--embed-code.html.twig * field--default--field-embed-code.html.twig * field--default.html.twig * field--theme-ds-field-default.html.twig * field--paragraph--field-embed-code--embed-code.html.twig * field--paragraph--field-embed-code.html.twig * field--paragraph--embed-code.html.twig * field--field-embed-code.html.twig * field--text-long.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-embed-code field--type-text-long field--label-hidden field--item"><iframe src="https://www.geogebra.org/classic/gjencrn6?embed" width="800" height="600" allowfullscreen="" frameborder="0"></iframe></div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> </div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-cover-image--resource-tutorial.html.twig * field--node--field-cover-image.html.twig * field--node--resource-tutorial.html.twig * field--field-cover-image.html.twig * field--image.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-cover-image field--type-image field--label-above"> <div class="field--label">Cover Image</div> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'image_formatter' --> <!-- BEGIN OUTPUT from 'core/modules/image/templates/image-formatter.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'image' --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/system/image.html.twig' --> <img src="/sites/default/files/up/tutorial/cover-image/2020-07/black-and-white-blur-book-business-240163.jpg" width="1280" height="720" alt="" typeof="foaf:Image" class="img-responsive" /> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/system/image.html.twig' --> <!-- END OUTPUT from 'core/modules/image/templates/image-formatter.html.twig' --> </div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-included-in-feeds--resource-tutorial.html.twig * field--node--field-included-in-feeds.html.twig * field--node--resource-tutorial.html.twig * field--field-included-in-feeds.html.twig * field--boolean.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-included-in-feeds field--type-boolean field--label-above"> <div class="field--label">Share in catalogue</div> <div class="field--item">On</div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-tags--resource-tutorial.html.twig * field--node--field-tags.html.twig * field--node--resource-tutorial.html.twig * field--field-tags.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-tags field--type-entity-reference field--label-above"> <div class="field--label">Tags</div> <div class="field--items"> <div class="field--item"><a href="/taxonomy/term/166" hreflang="en">Math</a></div> <div class="field--item"><a href="/taxonomy/term/167" hreflang="en">Algebra</a></div> <div class="field--item"><a href="/taxonomy/term/168" hreflang="en">Functions</a></div> </div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-top-bar-region-tutorials--resource-tutorial.html.twig * field--node--field-top-bar-region-tutorials.html.twig * field--node--resource-tutorial.html.twig * field--field-top-bar-region-tutorials.html.twig * field--markup.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-top-bar-region-tutorials field--type-markup field--label-above"> <div class="field--label">Top Bar Region - Tutorials</div> <div class="field--item"><div class="col-md-6 hidden-xs hidden-sm" id="top-bar-left"> <div class="btn-group"> <a class="btn btn-primary btn-sm" href="/forum/3/creating-and-sharing-resources" target="_blank">Documentation</a> <!--<a class="btn btn-primary btn-sm" href="#">Help</a>--> </div> </div> <div class="col-md-6 text-right" id="top-bar-right"></div> </div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-creative-commons-license--resource-tutorial.html.twig * field--node--field-creative-commons-license.html.twig * field--node--resource-tutorial.html.twig * field--field-creative-commons-license.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-creative-commons-license field--type-entity-reference field--label-above"> <div class="field--label">Creative Commons License</div> <div class="field--item"><a href="/taxonomy/term/54" hreflang="en">CC BY</a></div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-education-level--resource-tutorial.html.twig * field--node--field-education-level.html.twig * field--node--resource-tutorial.html.twig * field--field-education-level.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-education-level field--type-entity-reference field--label-above"> <div class="field--label">Education Level</div> <div class="field--item"><a href="/taxonomy/term/134" hreflang="en">High School</a></div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-educational-use--resource-tutorial.html.twig * field--node--field-educational-use.html.twig * field--node--resource-tutorial.html.twig * field--field-educational-use.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-educational-use field--type-entity-reference field--label-above"> <div class="field--label">Educational Use</div> <div class="field--item"><a href="/taxonomy/term/109" hreflang="en">Instruction</a></div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-material-type--resource-tutorial.html.twig * field--node--field-material-type.html.twig * field--node--resource-tutorial.html.twig * field--field-material-type.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-material-type field--type-entity-reference field--label-above"> <div class="field--label">Material Type</div> <div class="field--item"><a href="/taxonomy/term/130" hreflang="en">Reading Material</a></div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-subject-area--resource-tutorial.html.twig * field--node--field-subject-area.html.twig * field--node--resource-tutorial.html.twig * field--field-subject-area.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-subject-area field--type-entity-reference field--label-above"> <div class="field--label">Subject Area</div> <div class="field--item"><a href="/taxonomy/term/149" hreflang="en">Mathematics</a></div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-brief-description--resource-tutorial.html.twig * field--node--field-brief-description.html.twig * field--node--resource-tutorial.html.twig * field--field-brief-description.html.twig * field--string-long.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-brief-description field--type-string-long field--label-above"> <div class="field--label">Brief Description</div> <div class="field--item">A demonstration of the MathJax authoring capabilities. Content for this page has been sourced from OpenStax - Access for free at https://openstax.org/books/algebra-and-trigonometry/pages/1-introduction-to-prerequisites</div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--comment--resource-tutorial.html.twig * field--node--comment.html.twig * field--node--resource-tutorial.html.twig x field--comment.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'themes/custom/learnful-theme/templates/field--comment.html.twig' --> <section id="node-resource-tutorial-comment--4"> <p class="for-guest"><a href="/login">Login</a> or <a href="/signup/beta">register</a> to join the discussion.</p> <div id="comment-list"> <h2>Comments</h2> <p class="text-muted small">Be the first to comment!</p> </div> </section> <!-- END OUTPUT from 'themes/custom/learnful-theme/templates/field--comment.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-report-adaption--resource-tutorial.html.twig * field--node--field-report-adaption.html.twig * field--node--resource-tutorial.html.twig x field--field-report-adaption.html.twig * field--comment.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'themes/custom/learnful-theme/templates/field--field-report-adaption.html.twig' --> <section id="node-resource-tutorial-field-report-adaption--4"> <p class="for-guest"><a href="/login">Login</a> or <a href="/signup/beta">register</a> to share your adaptations.</p> <div id="comment-list"> <h2>List of adaptions</h2> <p class="text-muted small">Be the first to add your adaptation here!</p> </div> </section> <!-- END OUTPUT from 'themes/custom/learnful-theme/templates/field--field-report-adaption.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-top-bar-region-lesson-clon--resource-tutorial.html.twig * field--node--field-top-bar-region-lesson-clon.html.twig * field--node--resource-tutorial.html.twig * field--field-top-bar-region-lesson-clon.html.twig * field--markup.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-top-bar-region-lesson-clon field--type-markup field--label-above"> <div class="field--label">Top Bar Region - Lesson - Clone</div> <div class="field--item"><div class="col-md-6 hidden-xs hidden-sm" id="top-bar-left"> <div class="btn-group"> </div> </div> <div class="col-md-6 text-right" id="top-bar-right"></div></div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-remix-of--resource-tutorial.html.twig * field--node--field-remix-of.html.twig * field--node--resource-tutorial.html.twig * field--field-remix-of.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-remix-of field--type-entity-reference field--label-above"> <div class="field--label">Remix of</div> <div class="field--item"><a href="/lesson/143" hreflang="en">Functions and Function Notation</a></div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-display-in-portfolio--resource-tutorial.html.twig * field--node--field-display-in-portfolio.html.twig * field--node--resource-tutorial.html.twig * field--field-display-in-portfolio.html.twig * field--boolean.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-display-in-portfolio field--type-boolean field--label-above"> <div class="field--label">Display in Portfolio</div> <div class="field--item">Off</div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-license-is-derivative--resource-tutorial.html.twig * field--node--field-license-is-derivative.html.twig * field--node--resource-tutorial.html.twig * field--field-license-is-derivative.html.twig * field--boolean.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-license-is-derivative field--type-boolean field--label-above"> <div class="field--label">This work is a derivative</div> <div class="field--item">Off</div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-feedback-review--resource-tutorial.html.twig * field--node--field-feedback-review.html.twig * field--node--resource-tutorial.html.twig x field--field-feedback-review.html.twig * field--comment.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'themes/custom/learnful-theme/templates/field--field-feedback-review.html.twig' --> <section id="node-resource-tutorial-field-feedback-review--4"> <p class="for-guest"><a href="/login">Login</a> or <a href="/signup/beta">register</a> to engage in the review and feedback process.</p> <div id="comment-list"> <h2>Reviews and Feedback</h2> <p class="text-muted small">Be the first to review!</p> </div> </section> <!-- END OUTPUT from 'themes/custom/learnful-theme/templates/field--field-feedback-review.html.twig' --> Fri, 14 Aug 2020 17:44:34 +0000 Robin Shields 220 at https://learnful.ca https://learnful.ca/lesson/220#comments https://learnful.ca/lesson/220#comments https://learnful.ca/lesson/220#comments Calculus Question Set https://learnful.ca/h5p/158 <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--title--resource-h5p.html.twig x field--node--title.html.twig * field--node--resource-h5p.html.twig * field--title.html.twig * field--string.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'core/modules/node/templates/field--node--title.html.twig' --> <span>Calculus Question Set</span> <!-- END OUTPUT from 'core/modules/node/templates/field--node--title.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--uid--resource-h5p.html.twig x field--node--uid.html.twig * field--node--resource-h5p.html.twig * field--uid.html.twig * field--entity-reference.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'core/modules/node/templates/field--node--uid.html.twig' --> <span> <!-- THEME DEBUG --> <!-- THEME HOOK: 'username' --> <!-- BEGIN OUTPUT from 'core/modules/user/templates/username.html.twig' --> <a title="View user profile." href="/member/robinsheilds" lang="" about="/member/robinsheilds" typeof="schema:Person" property="schema:name" datatype="">Robin Shields</a> <!-- END OUTPUT from 'core/modules/user/templates/username.html.twig' --> </span> <!-- END OUTPUT from 'core/modules/node/templates/field--node--uid.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--created--resource-h5p.html.twig x field--node--created.html.twig * field--node--resource-h5p.html.twig * field--created.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'core/modules/node/templates/field--node--created.html.twig' --> <span>Fri, 07/10/2020 - 12:29</span> <!-- END OUTPUT from 'core/modules/node/templates/field--node--created.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'container' --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/system/container.html.twig' --> <div class="views-element-container form-group"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'eva_display_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/eva/templates/eva-display-entity-view.html.twig' --> <div class="view view-eva view-h5p-node-blocks view-id-h5p_node_blocks view-display-id-entity_view_1 js-view-dom-id-827921f64ba83ba11495b3c4205cf9076acc4d2ac34cad406998a7ba081cd319"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'views_view_unformatted' --> <!-- BEGIN OUTPUT from 'core/modules/views/templates/views-view-unformatted.html.twig' --> <div> <!-- THEME DEBUG --> <!-- THEME HOOK: 'views_view_fields' --> <!-- BEGIN OUTPUT from 'core/modules/views/templates/views-view-fields.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'views_view_field' --> <!-- BEGIN OUTPUT from 'core/modules/views/templates/views-view-field.html.twig' --> CC BY <!-- END OUTPUT from 'core/modules/views/templates/views-view-field.html.twig' --> <!-- END OUTPUT from 'core/modules/views/templates/views-view-fields.html.twig' --> </div> <!-- END OUTPUT from 'core/modules/views/templates/views-view-unformatted.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/eva/templates/eva-display-entity-view.html.twig' --> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/system/container.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'container' --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/system/container.html.twig' --> <div class="views-element-container form-group"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'eva_display_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/eva/templates/eva-display-entity-view.html.twig' --> <div class="view view-eva view-h5p-node-blocks view-id-h5p_node_blocks view-display-id-entity_view_2 js-view-dom-id-daf5f57856737c82c7e0295f97f679a2277990174366eb2d5c61d40d921953d7"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'views_view_unformatted' --> <!-- BEGIN OUTPUT from 'core/modules/views/templates/views-view-unformatted.html.twig' --> <div> <!-- THEME DEBUG --> <!-- THEME HOOK: 'views_view_fields' --> <!-- BEGIN OUTPUT from 'core/modules/views/templates/views-view-fields.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'views_view_field' --> <!-- BEGIN OUTPUT from 'core/modules/views/templates/views-view-field.html.twig' --> Question Set <!-- END OUTPUT from 'core/modules/views/templates/views-view-field.html.twig' --> <!-- END OUTPUT from 'core/modules/views/templates/views-view-fields.html.twig' --> </div> <!-- END OUTPUT from 'core/modules/views/templates/views-view-unformatted.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/eva/templates/eva-display-entity-view.html.twig' --> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/system/container.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'container' --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/system/container.html.twig' --> <div class="views-element-container form-group"></div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/system/container.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'links__node' --> <!-- FILE NAME SUGGESTIONS: * links--node.html.twig x links.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/system/links.html.twig' --> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/system/links.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-brief-description--resource-h5p.html.twig * field--node--field-brief-description.html.twig * field--node--resource-h5p.html.twig * field--field-brief-description.html.twig * field--string-long.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-brief-description field--type-string-long field--label-above"> <div class="field--label">Instructional Summary</div> <div class="field--item">A set of calculus questions that demonstrate MathJax/LaTeX support in H5P resources.</div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-cover-image--resource-h5p.html.twig * field--node--field-cover-image.html.twig * field--node--resource-h5p.html.twig * field--field-cover-image.html.twig * field--image.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-cover-image field--type-image field--label-above"> <div class="field--label">Cover Image</div> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'image_formatter' --> <!-- BEGIN OUTPUT from 'core/modules/image/templates/image-formatter.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'image' --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/system/image.html.twig' --> <img src="/sites/default/files/up/interactive/cover-image/2020-07/monochrome-photo-of-math-formulas-3729557.jpg" width="640" height="426" alt="" typeof="foaf:Image" class="img-responsive" /> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/system/image.html.twig' --> <!-- END OUTPUT from 'core/modules/image/templates/image-formatter.html.twig' --> </div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-included-in-feeds--resource-h5p.html.twig * field--node--field-included-in-feeds.html.twig * field--node--resource-h5p.html.twig * field--field-included-in-feeds.html.twig * field--boolean.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-included-in-feeds field--type-boolean field--label-above"> <div class="field--label">Share in catalogue</div> <div class="field--item">On</div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-tags--resource-h5p.html.twig * field--node--field-tags.html.twig * field--node--resource-h5p.html.twig * field--field-tags.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-tags field--type-entity-reference field--label-above"> <div class="field--label">Tags</div> <div class="field--items"> <div class="field--item"><a href="/taxonomy/term/169" hreflang="en">Calculus</a></div> <div class="field--item"><a href="/taxonomy/term/168" hreflang="en">Functions</a></div> <div class="field--item"><a href="/taxonomy/term/166" hreflang="en">Math</a></div> <div class="field--item"><a href="/taxonomy/term/226" hreflang="en">Differential Equations</a></div> </div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-top-bar-region-h5p--resource-h5p.html.twig * field--node--field-top-bar-region-h5p.html.twig * field--node--resource-h5p.html.twig * field--field-top-bar-region-h5p.html.twig * field--markup.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-top-bar-region-h5p field--type-markup field--label-above"> <div class="field--label">Top Bar Region</div> <div class="field--item"><div class="col-md-6 hidden-xs hidden-sm" id="top-bar-left"> <div class="btn-group"> <a class="btn btn-primary btn-sm" href="/forum/3/creating-and-sharing-resources" target="_blank">Documentation</a> <!--<a class="btn btn-primary btn-sm" href="#">Help</a>--> </div> </div> <div class="col-md-6 text-right" id="top-bar-right"></div></div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-h5p-content--resource-h5p.html.twig * field--node--field-h5p-content.html.twig * field--node--resource-h5p.html.twig * field--field-h5p-content.html.twig * field--h5p.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-h5p-content field--type-h5p field--label-above"> <div class="field--label">H5P Content</div> <div class="field--item"><div class="h5p-iframe-wrapper"><iframe enable-annotation id="h5p-iframe-26" class="h5p-iframe" data-content-id="26" frameborder="0" scrolling="no"></iframe></div></div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-h5p-settings-holder--resource-h5p.html.twig * field--node--field-h5p-settings-holder.html.twig * field--node--resource-h5p.html.twig * field--field-h5p-settings-holder.html.twig * field--markup.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-h5p-settings-holder field--type-markup field--label-above"> <div class="field--label">H5P Settings Holder</div> <div class="field--item"> </div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-educational-use--resource-h5p.html.twig * field--node--field-educational-use.html.twig * field--node--resource-h5p.html.twig * field--field-educational-use.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-educational-use field--type-entity-reference field--label-above"> <div class="field--label">Educational Use</div> <div class="field--item"><a href="/taxonomy/term/111" hreflang="en">Formative Assessment</a></div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-education-level--resource-h5p.html.twig * field--node--field-education-level.html.twig * field--node--resource-h5p.html.twig * field--field-education-level.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-education-level field--type-entity-reference field--label-above"> <div class="field--label">Education Level</div> <div class="field--item"><a href="/taxonomy/term/134" hreflang="en">High School</a></div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-material-type--resource-h5p.html.twig * field--node--field-material-type.html.twig * field--node--resource-h5p.html.twig * field--field-material-type.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-material-type field--type-entity-reference field--label-above"> <div class="field--label">Material Type</div> <div class="field--item"><a href="/taxonomy/term/116" hreflang="en">Assessment / Evaluation</a></div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-subject-area--resource-h5p.html.twig * field--node--field-subject-area.html.twig * field--node--resource-h5p.html.twig * field--field-subject-area.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-subject-area field--type-entity-reference field--label-above"> <div class="field--label">Subject Area</div> <div class="field--item"><a href="/taxonomy/term/149" hreflang="en">Mathematics</a></div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-report-adaption--resource-h5p.html.twig * field--node--field-report-adaption.html.twig * field--node--resource-h5p.html.twig x field--field-report-adaption.html.twig * field--comment.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'themes/custom/learnful-theme/templates/field--field-report-adaption.html.twig' --> <section id="node-resource-h5p-field-report-adaption"> <p class="for-guest"><a href="/login">Login</a> or <a href="/signup/beta">register</a> to share your adaptations.</p> <div id="comment-list"> <h2>List of adaptions</h2> <p class="text-muted small">Be the first to add your adaptation here!</p> </div> </section> <!-- END OUTPUT from 'themes/custom/learnful-theme/templates/field--field-report-adaption.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--comment--resource-h5p.html.twig * field--node--comment.html.twig * field--node--resource-h5p.html.twig x field--comment.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'themes/custom/learnful-theme/templates/field--comment.html.twig' --> <section> <p class="for-guest"><a href="/login">Login</a> or <a href="/signup/beta">register</a> to join the discussion.</p> <div id="comment-list"> <h2>Comments</h2> <p class="text-muted small">Be the first to comment!</p> </div> </section> <!-- END OUTPUT from 'themes/custom/learnful-theme/templates/field--comment.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-display-in-portfolio--resource-h5p.html.twig * field--node--field-display-in-portfolio.html.twig * field--node--resource-h5p.html.twig * field--field-display-in-portfolio.html.twig * field--boolean.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-display-in-portfolio field--type-boolean field--label-above"> <div class="field--label">Display in Portfolio</div> <div class="field--item">On</div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-top-bar-region-h5p-clone--resource-h5p.html.twig * field--node--field-top-bar-region-h5p-clone.html.twig * field--node--resource-h5p.html.twig * field--field-top-bar-region-h5p-clone.html.twig * field--markup.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-top-bar-region-h5p-clone field--type-markup field--label-above"> <div class="field--label">Top Bar Region - H5P - Clone</div> <div class="field--item"><div class="col-md-6 hidden-xs hidden-sm" id="top-bar-left"> <div class="btn-group"> </div> </div> <div class="col-md-6 text-right" id="top-bar-right"></div></div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-feedback-review--resource-h5p.html.twig * field--node--field-feedback-review.html.twig * field--node--resource-h5p.html.twig x field--field-feedback-review.html.twig * field--comment.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'themes/custom/learnful-theme/templates/field--field-feedback-review.html.twig' --> <section id="node-resource-h5p-field-feedback-review"> <p class="for-guest"><a href="/login">Login</a> or <a href="/signup/beta">register</a> to engage in the review and feedback process.</p> <div id="comment-list"> <h2>Reviews and Feedback</h2> <p class="text-muted small">Be the first to review!</p> </div> </section> <!-- END OUTPUT from 'themes/custom/learnful-theme/templates/field--field-feedback-review.html.twig' --> Fri, 10 Jul 2020 16:29:31 +0000 Robin Shields 158 at https://learnful.ca https://learnful.ca/h5p/158#comments https://learnful.ca/h5p/158#comments https://learnful.ca/h5p/158#comments Functions and Function Notation Quiz https://learnful.ca/h5p/145 <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--title--resource-h5p.html.twig x field--node--title.html.twig * field--node--resource-h5p.html.twig * field--title.html.twig * field--string.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'core/modules/node/templates/field--node--title.html.twig' --> <span>Functions and Function Notation Quiz</span> <!-- END OUTPUT from 'core/modules/node/templates/field--node--title.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--uid--resource-h5p.html.twig x field--node--uid.html.twig * field--node--resource-h5p.html.twig * field--uid.html.twig * field--entity-reference.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'core/modules/node/templates/field--node--uid.html.twig' --> <span> <!-- THEME DEBUG --> <!-- THEME HOOK: 'username' --> <!-- BEGIN OUTPUT from 'core/modules/user/templates/username.html.twig' --> <a title="View user profile." href="/member/learnful" lang="" about="/member/learnful" typeof="schema:Person" property="schema:name" datatype="">Help@Learnful</a> <!-- END OUTPUT from 'core/modules/user/templates/username.html.twig' --> </span> <!-- END OUTPUT from 'core/modules/node/templates/field--node--uid.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--created--resource-h5p.html.twig x field--node--created.html.twig * field--node--resource-h5p.html.twig * field--created.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'core/modules/node/templates/field--node--created.html.twig' --> <span>Fri, 07/03/2020 - 01:14</span> <!-- END OUTPUT from 'core/modules/node/templates/field--node--created.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'container' --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/system/container.html.twig' --> <div class="views-element-container form-group"></div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/system/container.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'container' --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/system/container.html.twig' --> <div class="views-element-container form-group"></div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/system/container.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'container' --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/system/container.html.twig' --> <div class="views-element-container form-group"></div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/system/container.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'links__node' --> <!-- FILE NAME SUGGESTIONS: * links--node.html.twig x links.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/system/links.html.twig' --> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/system/links.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-cover-image--resource-h5p.html.twig * field--node--field-cover-image.html.twig * field--node--resource-h5p.html.twig * field--field-cover-image.html.twig * field--image.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-cover-image field--type-image field--label-above"> <div class="field--label">Cover Image</div> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'image_formatter' --> <!-- BEGIN OUTPUT from 'core/modules/image/templates/image-formatter.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'image' --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/system/image.html.twig' --> <img src="/sites/default/files/default_images/nocoverimage_0.png" width="480" height="480" alt="" typeof="foaf:Image" class="img-responsive" /> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/system/image.html.twig' --> <!-- END OUTPUT from 'core/modules/image/templates/image-formatter.html.twig' --> </div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-included-in-feeds--resource-h5p.html.twig * field--node--field-included-in-feeds.html.twig * field--node--resource-h5p.html.twig * field--field-included-in-feeds.html.twig * field--boolean.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-included-in-feeds field--type-boolean field--label-above"> <div class="field--label">Share in catalogue</div> <div class="field--item">Off</div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-tags--resource-h5p.html.twig * field--node--field-tags.html.twig * field--node--resource-h5p.html.twig * field--field-tags.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-tags field--type-entity-reference field--label-above"> <div class="field--label">Tags</div> <div class="field--items"> <div class="field--item"><a href="/taxonomy/term/167" hreflang="en">Algebra</a></div> <div class="field--item"><a href="/taxonomy/term/168" hreflang="en">Functions</a></div> <div class="field--item"><a href="/taxonomy/term/166" hreflang="en">Math</a></div> </div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-top-bar-region-h5p--resource-h5p.html.twig * field--node--field-top-bar-region-h5p.html.twig * field--node--resource-h5p.html.twig * field--field-top-bar-region-h5p.html.twig * field--markup.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-top-bar-region-h5p field--type-markup field--label-above"> <div class="field--label">Top Bar Region</div> <div class="field--item"><div class="col-md-6 hidden-xs hidden-sm" id="top-bar-left"> <div class="btn-group"> <a class="btn btn-primary btn-sm" href="/forum/3/creating-and-sharing-resources" target="_blank">Documentation</a> <!--<a class="btn btn-primary btn-sm" href="#">Help</a>--> </div> </div> <div class="col-md-6 text-right" id="top-bar-right"></div></div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-h5p-content--resource-h5p.html.twig * field--node--field-h5p-content.html.twig * field--node--resource-h5p.html.twig * field--field-h5p-content.html.twig * field--h5p.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-h5p-content field--type-h5p field--label-above"> <div class="field--label">H5P Content</div> <div class="field--item"><div class="h5p-iframe-wrapper"><iframe enable-annotation id="h5p-iframe-24" class="h5p-iframe" data-content-id="24" frameborder="0" scrolling="no"></iframe></div></div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-h5p-settings-holder--resource-h5p.html.twig * field--node--field-h5p-settings-holder.html.twig * field--node--resource-h5p.html.twig * field--field-h5p-settings-holder.html.twig * field--markup.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-h5p-settings-holder field--type-markup field--label-above"> <div class="field--label">H5P Settings Holder</div> <div class="field--item"> </div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-educational-use--resource-h5p.html.twig * field--node--field-educational-use.html.twig * field--node--resource-h5p.html.twig * field--field-educational-use.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-educational-use field--type-entity-reference field--label-above"> <div class="field--label">Educational Use</div> <div class="field--item"><a href="/taxonomy/term/111" hreflang="en">Formative Assessment</a></div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-education-level--resource-h5p.html.twig * field--node--field-education-level.html.twig * field--node--resource-h5p.html.twig * field--field-education-level.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-education-level field--type-entity-reference field--label-above"> <div class="field--label">Education Level</div> <div class="field--item"><a href="/taxonomy/term/134" hreflang="en">High School</a></div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-material-type--resource-h5p.html.twig * field--node--field-material-type.html.twig * field--node--resource-h5p.html.twig * field--field-material-type.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-material-type field--type-entity-reference field--label-above"> <div class="field--label">Material Type</div> <div class="field--item"><a href="/taxonomy/term/116" hreflang="en">Assessment / Evaluation</a></div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-subject-area--resource-h5p.html.twig * field--node--field-subject-area.html.twig * field--node--resource-h5p.html.twig * field--field-subject-area.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-subject-area field--type-entity-reference field--label-above"> <div class="field--label">Subject Area</div> <div class="field--item"><a href="/taxonomy/term/149" hreflang="en">Mathematics</a></div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-report-adaption--resource-h5p.html.twig * field--node--field-report-adaption.html.twig * field--node--resource-h5p.html.twig x field--field-report-adaption.html.twig * field--comment.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'themes/custom/learnful-theme/templates/field--field-report-adaption.html.twig' --> <section id="node-resource-h5p-field-report-adaption--2"> <p class="for-guest"><a href="/login">Login</a> or <a href="/signup/beta">register</a> to share your adaptations.</p> <div id="comment-list"> <h2>List of adaptions</h2> <p class="text-muted small">Be the first to add your adaptation here!</p> </div> </section> <!-- END OUTPUT from 'themes/custom/learnful-theme/templates/field--field-report-adaption.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--comment--resource-h5p.html.twig * field--node--comment.html.twig * field--node--resource-h5p.html.twig x field--comment.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'themes/custom/learnful-theme/templates/field--comment.html.twig' --> <section> <p class="for-guest"><a href="/login">Login</a> or <a href="/signup/beta">register</a> to join the discussion.</p> <div id="comment-list"> <h2>Comments</h2> <p class="text-muted small">Be the first to comment!</p> </div> </section> <!-- END OUTPUT from 'themes/custom/learnful-theme/templates/field--comment.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-top-bar-region-h5p-clone--resource-h5p.html.twig * field--node--field-top-bar-region-h5p-clone.html.twig * field--node--resource-h5p.html.twig * field--field-top-bar-region-h5p-clone.html.twig * field--markup.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-top-bar-region-h5p-clone field--type-markup field--label-above"> <div class="field--label">Top Bar Region - H5P - Clone</div> <div class="field--item"><div class="col-md-6 hidden-xs hidden-sm" id="top-bar-left"> <div class="btn-group"> </div> </div> <div class="col-md-6 text-right" id="top-bar-right"></div></div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-feedback-review--resource-h5p.html.twig * field--node--field-feedback-review.html.twig * field--node--resource-h5p.html.twig x field--field-feedback-review.html.twig * field--comment.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'themes/custom/learnful-theme/templates/field--field-feedback-review.html.twig' --> <section id="node-resource-h5p-field-feedback-review--2"> <p class="for-guest"><a href="/login">Login</a> or <a href="/signup/beta">register</a> to engage in the review and feedback process.</p> <div id="comment-list"> <h2>Reviews and Feedback</h2> <p class="text-muted small">Be the first to review!</p> </div> </section> <!-- END OUTPUT from 'themes/custom/learnful-theme/templates/field--field-feedback-review.html.twig' --> Fri, 03 Jul 2020 05:14:30 +0000 Help@Learnful 145 at https://learnful.ca https://learnful.ca/h5p/145#comments https://learnful.ca/h5p/145#comments https://learnful.ca/h5p/145#comments Determine if the relationship is a function https://learnful.ca/h5p/144 <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--title--resource-h5p.html.twig x field--node--title.html.twig * field--node--resource-h5p.html.twig * field--title.html.twig * field--string.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'core/modules/node/templates/field--node--title.html.twig' --> <span>Determine if the relationship is a function</span> <!-- END OUTPUT from 'core/modules/node/templates/field--node--title.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--uid--resource-h5p.html.twig x field--node--uid.html.twig * field--node--resource-h5p.html.twig * field--uid.html.twig * field--entity-reference.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'core/modules/node/templates/field--node--uid.html.twig' --> <span> <!-- THEME DEBUG --> <!-- THEME HOOK: 'username' --> <!-- BEGIN OUTPUT from 'core/modules/user/templates/username.html.twig' --> <a title="View user profile." href="/member/learnful" lang="" about="/member/learnful" typeof="schema:Person" property="schema:name" datatype="">Help@Learnful</a> <!-- END OUTPUT from 'core/modules/user/templates/username.html.twig' --> </span> <!-- END OUTPUT from 'core/modules/node/templates/field--node--uid.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--created--resource-h5p.html.twig x field--node--created.html.twig * field--node--resource-h5p.html.twig * field--created.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'core/modules/node/templates/field--node--created.html.twig' --> <span>Fri, 07/03/2020 - 00:44</span> <!-- END OUTPUT from 'core/modules/node/templates/field--node--created.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'container' --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/system/container.html.twig' --> <div class="views-element-container form-group"></div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/system/container.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'container' --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/system/container.html.twig' --> <div class="views-element-container form-group"></div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/system/container.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'container' --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/system/container.html.twig' --> <div class="views-element-container form-group"></div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/system/container.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'links__node' --> <!-- FILE NAME SUGGESTIONS: * links--node.html.twig x links.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/system/links.html.twig' --> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/system/links.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-brief-description--resource-h5p.html.twig * field--node--field-brief-description.html.twig * field--node--resource-h5p.html.twig * field--field-brief-description.html.twig * field--string-long.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-brief-description field--type-string-long field--label-above"> <div class="field--label">Instructional Summary</div> <div class="field--item">These examples are sourced from OpenStax - Access for free at https://openstax.org/books/algebra-and-trigonometry/pages/1-introduction-to-prerequisites</div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-cover-image--resource-h5p.html.twig * field--node--field-cover-image.html.twig * field--node--resource-h5p.html.twig * field--field-cover-image.html.twig * field--image.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-cover-image field--type-image field--label-above"> <div class="field--label">Cover Image</div> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'image_formatter' --> <!-- BEGIN OUTPUT from 'core/modules/image/templates/image-formatter.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'image' --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/system/image.html.twig' --> <img src="/sites/default/files/default_images/nocoverimage_0.png" width="480" height="480" alt="" typeof="foaf:Image" class="img-responsive" /> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/system/image.html.twig' --> <!-- END OUTPUT from 'core/modules/image/templates/image-formatter.html.twig' --> </div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-included-in-feeds--resource-h5p.html.twig * field--node--field-included-in-feeds.html.twig * field--node--resource-h5p.html.twig * field--field-included-in-feeds.html.twig * field--boolean.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-included-in-feeds field--type-boolean field--label-above"> <div class="field--label">Share in catalogue</div> <div class="field--item">Off</div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-tags--resource-h5p.html.twig * field--node--field-tags.html.twig * field--node--resource-h5p.html.twig * field--field-tags.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-tags field--type-entity-reference field--label-above"> <div class="field--label">Tags</div> <div class="field--items"> <div class="field--item"><a href="/taxonomy/term/168" hreflang="en">Functions</a></div> <div class="field--item"><a href="/taxonomy/term/166" hreflang="en">Math</a></div> </div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-top-bar-region-h5p--resource-h5p.html.twig * field--node--field-top-bar-region-h5p.html.twig * field--node--resource-h5p.html.twig * field--field-top-bar-region-h5p.html.twig * field--markup.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-top-bar-region-h5p field--type-markup field--label-above"> <div class="field--label">Top Bar Region</div> <div class="field--item"><div class="col-md-6 hidden-xs hidden-sm" id="top-bar-left"> <div class="btn-group"> <a class="btn btn-primary btn-sm" href="/forum/3/creating-and-sharing-resources" target="_blank">Documentation</a> <!--<a class="btn btn-primary btn-sm" href="#">Help</a>--> </div> </div> <div class="col-md-6 text-right" id="top-bar-right"></div></div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-h5p-content--resource-h5p.html.twig * field--node--field-h5p-content.html.twig * field--node--resource-h5p.html.twig * field--field-h5p-content.html.twig * field--h5p.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-h5p-content field--type-h5p field--label-above"> <div class="field--label">H5P Content</div> <div class="field--item"><div class="h5p-iframe-wrapper"><iframe enable-annotation id="h5p-iframe-23" class="h5p-iframe" data-content-id="23" frameborder="0" scrolling="no"></iframe></div></div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-h5p-settings-holder--resource-h5p.html.twig * field--node--field-h5p-settings-holder.html.twig * field--node--resource-h5p.html.twig * field--field-h5p-settings-holder.html.twig * field--markup.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-h5p-settings-holder field--type-markup field--label-above"> <div class="field--label">H5P Settings Holder</div> <div class="field--item"> </div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-educational-use--resource-h5p.html.twig * field--node--field-educational-use.html.twig * field--node--resource-h5p.html.twig * field--field-educational-use.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-educational-use field--type-entity-reference field--label-above"> <div class="field--label">Educational Use</div> <div class="field--item"><a href="/taxonomy/term/111" hreflang="en">Formative Assessment</a></div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-education-level--resource-h5p.html.twig * field--node--field-education-level.html.twig * field--node--resource-h5p.html.twig * field--field-education-level.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-education-level field--type-entity-reference field--label-above"> <div class="field--label">Education Level</div> <div class="field--item"><a href="/taxonomy/term/134" hreflang="en">High School</a></div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-material-type--resource-h5p.html.twig * field--node--field-material-type.html.twig * field--node--resource-h5p.html.twig * field--field-material-type.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-material-type field--type-entity-reference field--label-above"> <div class="field--label">Material Type</div> <div class="field--item"><a href="/taxonomy/term/117" hreflang="en">Homework / Assignment</a></div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-subject-area--resource-h5p.html.twig * field--node--field-subject-area.html.twig * field--node--resource-h5p.html.twig * field--field-subject-area.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-subject-area field--type-entity-reference field--label-above"> <div class="field--label">Subject Area</div> <div class="field--item"><a href="/taxonomy/term/149" hreflang="en">Mathematics</a></div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-report-adaption--resource-h5p.html.twig * field--node--field-report-adaption.html.twig * field--node--resource-h5p.html.twig x field--field-report-adaption.html.twig * field--comment.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'themes/custom/learnful-theme/templates/field--field-report-adaption.html.twig' --> <section id="node-resource-h5p-field-report-adaption--3"> <p class="for-guest"><a href="/login">Login</a> or <a href="/signup/beta">register</a> to share your adaptations.</p> <div id="comment-list"> <h2>List of adaptions</h2> <p class="text-muted small">Be the first to add your adaptation here!</p> </div> </section> <!-- END OUTPUT from 'themes/custom/learnful-theme/templates/field--field-report-adaption.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--comment--resource-h5p.html.twig * field--node--comment.html.twig * field--node--resource-h5p.html.twig x field--comment.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'themes/custom/learnful-theme/templates/field--comment.html.twig' --> <section> <p class="for-guest"><a href="/login">Login</a> or <a href="/signup/beta">register</a> to join the discussion.</p> <div id="comment-list"> <h2>Comments</h2> <p class="text-muted small">Be the first to comment!</p> </div> </section> <!-- END OUTPUT from 'themes/custom/learnful-theme/templates/field--comment.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-top-bar-region-h5p-clone--resource-h5p.html.twig * field--node--field-top-bar-region-h5p-clone.html.twig * field--node--resource-h5p.html.twig * field--field-top-bar-region-h5p-clone.html.twig * field--markup.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-top-bar-region-h5p-clone field--type-markup field--label-above"> <div class="field--label">Top Bar Region - H5P - Clone</div> <div class="field--item"><div class="col-md-6 hidden-xs hidden-sm" id="top-bar-left"> <div class="btn-group"> </div> </div> <div class="col-md-6 text-right" id="top-bar-right"></div></div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-feedback-review--resource-h5p.html.twig * field--node--field-feedback-review.html.twig * field--node--resource-h5p.html.twig x field--field-feedback-review.html.twig * field--comment.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'themes/custom/learnful-theme/templates/field--field-feedback-review.html.twig' --> <section id="node-resource-h5p-field-feedback-review--3"> <p class="for-guest"><a href="/login">Login</a> or <a href="/signup/beta">register</a> to engage in the review and feedback process.</p> <div id="comment-list"> <h2>Reviews and Feedback</h2> <p class="text-muted small">Be the first to review!</p> </div> </section> <!-- END OUTPUT from 'themes/custom/learnful-theme/templates/field--field-feedback-review.html.twig' --> Fri, 03 Jul 2020 04:44:46 +0000 Help@Learnful 144 at https://learnful.ca https://learnful.ca/h5p/144#comments https://learnful.ca/h5p/144#comments https://learnful.ca/h5p/144#comments Functions and Function Notation https://learnful.ca/lesson/143 <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--title--resource-tutorial.html.twig x field--node--title.html.twig * field--node--resource-tutorial.html.twig * field--title.html.twig * field--string.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'core/modules/node/templates/field--node--title.html.twig' --> <span>Functions and Function Notation</span> <!-- END OUTPUT from 'core/modules/node/templates/field--node--title.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--uid--resource-tutorial.html.twig x field--node--uid.html.twig * field--node--resource-tutorial.html.twig * field--uid.html.twig * field--entity-reference.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'core/modules/node/templates/field--node--uid.html.twig' --> <span> <!-- THEME DEBUG --> <!-- THEME HOOK: 'username' --> <!-- BEGIN OUTPUT from 'core/modules/user/templates/username.html.twig' --> <a title="View user profile." href="/member/learnful" lang="" about="/member/learnful" typeof="schema:Person" property="schema:name" datatype="">Help@Learnful</a> <!-- END OUTPUT from 'core/modules/user/templates/username.html.twig' --> </span> <!-- END OUTPUT from 'core/modules/node/templates/field--node--uid.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--created--resource-tutorial.html.twig x field--node--created.html.twig * field--node--resource-tutorial.html.twig * field--created.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'core/modules/node/templates/field--node--created.html.twig' --> <span>Thu, 07/02/2020 - 23:37</span> <!-- END OUTPUT from 'core/modules/node/templates/field--node--created.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'links__node' --> <!-- FILE NAME SUGGESTIONS: * links--node.html.twig x links.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/system/links.html.twig' --> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/system/links.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-content-blocks--resource-tutorial.html.twig * field--node--field-content-blocks.html.twig * field--node--resource-tutorial.html.twig * field--field-content-blocks.html.twig * field--entity-reference-revisions.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-content-blocks field--type-entity-reference-revisions field--label-above"> <div class="field--label">Content Blocks</div> <div class="field--items"> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--paragraph--326.html.twig * ds-1col--paragraph-basic-text-block-default.html.twig * ds-1col--paragraph-basic-text-block.html.twig * ds-1col--paragraph-default.html.twig * ds-1col--paragraph.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div class="paragraph paragraph--type-basic-text-block paragraph--view-mode-default ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--expert--paragraph--field-section-title--basic-text-block.html.twig * field--expert--paragraph--basic-text-block.html.twig * field--expert--paragraph--field-section-title.html.twig * field--expert--field-section-title--basic-text-block.html.twig * field--expert--basic-text-block.html.twig * field--expert--field-section-title.html.twig * field--expert.html.twig * field--ds-field-expert.html.twig * field--paragraph--field-section-title--basic-text-block.html.twig * field--paragraph--field-section-title.html.twig * field--paragraph--basic-text-block.html.twig * field--field-section-title.html.twig * field--string.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <h2 class="section-title" > Learning Objectives</h2> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--default--paragraph--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--default--paragraph--basic-text-block.html.twig * field--default--paragraph--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--default--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--default--basic-text-block.html.twig * field--default--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--default.html.twig * field--theme-ds-field-default.html.twig * field--paragraph--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--paragraph--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--paragraph--basic-text-block.html.twig * field--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--ds.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-dynamic-token-fieldparagraph-paragraph-text-block field--type-ds field--label-hidden field--item"><div class="p-textblock width-default" data-bgcolor="#FFFFFF"><div class="tex2jax_process"><p>In this section, you will:</p> <ul> <li>Determine whether a relation represents a function.</li> <li>Find the value of a function.</li> <li>Determine whether a function is one-to-one.</li> <li>Use the vertical line test to identify functions.</li> <li>Graph the functions listed in the library of functions.</li> </ul> <p>A jetliner changes altitude as its distance from the starting point of a flight increases. The weight of a growing child increases with time. In each case, one quantity depends on another. There is a relationship between the two quantities that we can describe, analyze, and use to make predictions. In this section, we will analyze such relationships.</p> </div></div></div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--paragraph--327.html.twig * ds-1col--paragraph-basic-text-block-default.html.twig * ds-1col--paragraph-basic-text-block.html.twig * ds-1col--paragraph-default.html.twig * ds-1col--paragraph.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div class="paragraph paragraph--type-basic-text-block paragraph--view-mode-default ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--expert--paragraph--field-section-title--basic-text-block.html.twig * field--expert--paragraph--basic-text-block.html.twig * field--expert--paragraph--field-section-title.html.twig * field--expert--field-section-title--basic-text-block.html.twig * field--expert--basic-text-block.html.twig * field--expert--field-section-title.html.twig * field--expert.html.twig * field--ds-field-expert.html.twig * field--paragraph--field-section-title--basic-text-block.html.twig * field--paragraph--field-section-title.html.twig * field--paragraph--basic-text-block.html.twig * field--field-section-title.html.twig * field--string.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <h2 class="section-title" > Determining Whether a Relation Represents a Function</h2> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--default--paragraph--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--default--paragraph--basic-text-block.html.twig * field--default--paragraph--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--default--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--default--basic-text-block.html.twig * field--default--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--default.html.twig * field--theme-ds-field-default.html.twig * field--paragraph--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--paragraph--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--paragraph--basic-text-block.html.twig * field--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--ds.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-dynamic-token-fieldparagraph-paragraph-text-block field--type-ds field--label-hidden field--item"><div class="p-textblock width-default" data-bgcolor="#FFFFFF"><div class="tex2jax_process"><p>A relation is a set of ordered pairs. The set consisting of the first components of each ordered pair is called the <strong>domain </strong>and the set consisting of the second components of each ordered pair is called the <strong>range</strong>. Consider the following set of ordered pairs. The first numbers in each pair are the first five natural numbers. The second number in each pair is twice that of the first.</p> <p>$$\{(1,\text{ }2),\text{ }(2,\text{ }4),\text{ }(3,\text{ }6),\text{ }(4,\text{ }8),\text{ }(5,\text{ }10)\}$$</p> <p>The domain is \(\{1,\text{ }2,\text{ }3,\text{ }4,\text{ }5\}\). The range is \(\{2,\text{ }4,\text{ }6,\text{ }8,\text{ }10\}\).</p> <p>Note that each value in the domain is also known as an <strong>input</strong> value, or independent variable, and is often labeled with the lowercase letter \(x\). Each value in the range is also known as an <strong>output</strong> value, or dependent variable, and is often labeled lowercase letter \(y\).</p> <p>A function \(f\) is a relation that assigns a single value in the range to each value in the domain<em>.</em> In other words, no <em>x</em>-values are repeated. For our example that relates the first five natural numbers to numbers double their values, this relation is a function because each element in the domain, \(\{1, 2, 3, 4, 5\}\), is paired with exactly one element in the range, \(\{2, 4, 6, 8, 10\}\).</p> <p>Now let’s consider the set of ordered pairs that relates the terms “even” and “odd” to the first five natural numbers. It would appear as</p> <p>$$\{{(\text{odd},\text{ }1),\text{ }(\text{even},\text{ }2),\text{ }(\text{odd},\text{ }3),\text{ }(\text{even},\text{ }4),\text{ }(\text{odd},\text{ }5)}\}$$</p> <p>Notice that each element in the domain, \(\{even, odd\}\) is <em>not</em> paired with exactly one element in the range, \(\{1, 2, 3, 4, 5\}\). For example, the term “odd” corresponds to three values from the range, \(\{1, 3, 5\}\) and the term “even” corresponds to two values from the range, \(\{2, 4\}\). This violates the definition of a function, so this relation is not a function.</p> <p>Figure 1 compares relations that are functions and not functions.</p> </div></div></div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--paragraph--328.html.twig * ds-1col--paragraph-image-with-caption-default.html.twig * ds-1col--paragraph-image-with-caption.html.twig * ds-1col--paragraph-default.html.twig * ds-1col--paragraph.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div class="paragraph paragraph--type-image-with-caption paragraph--view-mode-default ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field_group_html_element' --> <!-- FILE NAME SUGGESTIONS: * field-group-html-element--paragraph--image-with-caption--group-p-imagecaption.html.twig * field-group-html-element--paragraph--image-with-caption--div.html.twig * field-group-html-element--paragraph--group-p-imagecaption.html.twig * field-group-html-element--paragraph--image-with-caption.html.twig * field-group-html-element--paragraph--div.html.twig * field-group-html-element--group-p-imagecaption.html.twig * field-group-html-element--image-with-caption.html.twig * field-group-html-element--paragraph.html.twig * field-group-html-element--div.html.twig x field-group-html-element.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/field_group/templates/field-group-html-element.html.twig' --> <div class="p-imagecaption width-default"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--expert--paragraph--field-image--image-with-caption.html.twig * field--expert--paragraph--image-with-caption.html.twig * field--expert--paragraph--field-image.html.twig * field--expert--field-image--image-with-caption.html.twig * field--expert--image-with-caption.html.twig * field--expert--field-image.html.twig * field--expert.html.twig * field--ds-field-expert.html.twig * field--paragraph--field-image--image-with-caption.html.twig * field--paragraph--field-image.html.twig * field--paragraph--image-with-caption.html.twig * field--field-image.html.twig * field--image.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <figure width="narrow"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'colorbox_formatter' --> <!-- BEGIN OUTPUT from 'modules/contrib/colorbox/templates/colorbox-formatter.html.twig' --> <a href="https://learnful.ca/sites/default/files/up/para/field-image/2020-07/78/d47bde493af93fa714bfc3dbe2a30008d2b7a5f0.jpeg" title="Figure 1 (a) This relationship is a function because each input is associated with a single output. Note that input  q  and  r  both give output  n.  (b) This relationship is also a function. In this case, each input is associated with a single output." data-colorbox-gallery="" class="colorbox" data-cbox-img-attrs="{&quot;alt&quot;:&quot;Three relations that demonstrate what constitute a function.&quot;}"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'image_style' --> <!-- BEGIN OUTPUT from 'core/modules/image/templates/image-style.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'image' --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/system/image.html.twig' --> <img src="/sites/default/files/styles/xxl/public/up/para/field-image/2020-07/78/d47bde493af93fa714bfc3dbe2a30008d2b7a5f0.jpeg?itok=14jOLkeR" width="1400" height="349" alt="Three relations that demonstrate what constitute a function." typeof="foaf:Image" class="img-responsive" /> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/system/image.html.twig' --> <!-- END OUTPUT from 'core/modules/image/templates/image-style.html.twig' --> </a> <!-- END OUTPUT from 'modules/contrib/colorbox/templates/colorbox-formatter.html.twig' --> </figure> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--expert--paragraph--field-image-caption--image-with-caption.html.twig * field--expert--paragraph--image-with-caption.html.twig * field--expert--paragraph--field-image-caption.html.twig * field--expert--field-image-caption--image-with-caption.html.twig * field--expert--image-with-caption.html.twig * field--expert--field-image-caption.html.twig * field--expert.html.twig * field--ds-field-expert.html.twig * field--paragraph--field-image-caption--image-with-caption.html.twig * field--paragraph--field-image-caption.html.twig * field--paragraph--image-with-caption.html.twig * field--field-image-caption.html.twig * field--text.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <figcaption width="narrow"> <div class="tex2jax_process"><p>Figure 1 (a) This relationship is a function because each input is associated with a single output. Note that input  q  and  r  both give output  n.  (b) This relationship is also a function. In this case, each input is associated with a single output.</p> </div> </figcaption> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/field_group/templates/field-group-html-element.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--paragraph--329.html.twig * ds-1col--paragraph-basic-text-block-default.html.twig * ds-1col--paragraph-basic-text-block.html.twig * ds-1col--paragraph-default.html.twig * ds-1col--paragraph.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div class="paragraph paragraph--type-basic-text-block paragraph--view-mode-default ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--expert--paragraph--field-section-title--basic-text-block.html.twig * field--expert--paragraph--basic-text-block.html.twig * field--expert--paragraph--field-section-title.html.twig * field--expert--field-section-title--basic-text-block.html.twig * field--expert--basic-text-block.html.twig * field--expert--field-section-title.html.twig * field--expert.html.twig * field--ds-field-expert.html.twig * field--paragraph--field-section-title--basic-text-block.html.twig * field--paragraph--field-section-title.html.twig * field--paragraph--basic-text-block.html.twig * field--field-section-title.html.twig * field--string.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <h2 class="section-title" > Functions</h2> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--default--paragraph--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--default--paragraph--basic-text-block.html.twig * field--default--paragraph--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--default--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--default--basic-text-block.html.twig * field--default--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--default.html.twig * field--theme-ds-field-default.html.twig * field--paragraph--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--paragraph--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--paragraph--basic-text-block.html.twig * field--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--ds.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-dynamic-token-fieldparagraph-paragraph-text-block field--type-ds field--label-hidden field--item"><div class="p-textblock width-default" data-bgcolor="#FFFFFF"><div class="tex2jax_process"><p>A <strong>function </strong>is a relation in which each possible input value leads to exactly one output value. We say “the output is a function of the input.”</p> <p>The input values make up the <strong>domain</strong>, and the output values make up the <strong>range</strong>.</p> </div></div></div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--paragraph--330.html.twig * ds-1col--paragraph-basic-text-block-default.html.twig * ds-1col--paragraph-basic-text-block.html.twig * ds-1col--paragraph-default.html.twig * ds-1col--paragraph.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div class="paragraph paragraph--type-basic-text-block paragraph--view-mode-default ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--default--paragraph--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--default--paragraph--basic-text-block.html.twig * field--default--paragraph--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--default--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--default--basic-text-block.html.twig * field--default--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--default.html.twig * field--theme-ds-field-default.html.twig * field--paragraph--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--paragraph--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--paragraph--basic-text-block.html.twig * field--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--ds.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-dynamic-token-fieldparagraph-paragraph-text-block field--type-ds field--label-hidden field--item"><div class="p-textblock width-default" data-bgcolor="#FFFFFF"><div class="tex2jax_process"><h3>Examples</h3> <p>Given a relationship between two quantities, determine whether the relationship is a function.</p> </div></div></div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--paragraph--331.html.twig * ds-1col--paragraph-interactive-content-h5p--default.html.twig * ds-1col--paragraph-interactive-content-h5p-.html.twig * ds-1col--paragraph-default.html.twig * ds-1col--paragraph.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div class="paragraph paragraph--type-interactive-content-h5p- paragraph--view-mode-default ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--default--paragraph--field-interactive-content--interactive-content-h5p-.html.twig * field--default--paragraph--interactive-content-h5p-.html.twig * field--default--paragraph--field-interactive-content.html.twig * field--default--field-interactive-content--interactive-content-h5p-.html.twig * field--default--interactive-content-h5p-.html.twig * field--default--field-interactive-content.html.twig * field--default.html.twig * field--theme-ds-field-default.html.twig * field--paragraph--field-interactive-content--interactive-content-h5p-.html.twig * field--paragraph--field-interactive-content.html.twig * field--paragraph--interactive-content-h5p-.html.twig * field--field-interactive-content.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-interactive-content field--type-entity-reference field--label-hidden field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--node--144.html.twig * ds-1col--node-resource-h5p-teaser.html.twig * ds-1col--node-resource-h5p.html.twig * ds-1col--node-teaser.html.twig * ds-1col--node.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div data-history-node-id="144" class="node node--type-resource-h5p node--view-mode-teaser ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--default--node--field-h5p-content--resource-h5p.html.twig * field--default--node--resource-h5p.html.twig * field--default--node--field-h5p-content.html.twig * field--default--field-h5p-content--resource-h5p.html.twig * field--default--resource-h5p.html.twig * field--default--field-h5p-content.html.twig * field--default.html.twig * field--theme-ds-field-default.html.twig * field--node--field-h5p-content--resource-h5p.html.twig * field--node--field-h5p-content.html.twig * field--node--resource-h5p.html.twig * field--field-h5p-content.html.twig * field--h5p.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-h5p-content field--type-h5p field--label-hidden field--item"><div class="h5p-iframe-wrapper"><iframe enable-annotation id="h5p-iframe-23" class="h5p-iframe" data-content-id="23" frameborder="0" scrolling="no"></iframe></div></div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--paragraph--332.html.twig * ds-1col--paragraph-basic-text-block-default.html.twig * ds-1col--paragraph-basic-text-block.html.twig * ds-1col--paragraph-default.html.twig * ds-1col--paragraph.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div class="paragraph paragraph--type-basic-text-block paragraph--view-mode-default ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--expert--paragraph--field-section-title--basic-text-block.html.twig * field--expert--paragraph--basic-text-block.html.twig * field--expert--paragraph--field-section-title.html.twig * field--expert--field-section-title--basic-text-block.html.twig * field--expert--basic-text-block.html.twig * field--expert--field-section-title.html.twig * field--expert.html.twig * field--ds-field-expert.html.twig * field--paragraph--field-section-title--basic-text-block.html.twig * field--paragraph--field-section-title.html.twig * field--paragraph--basic-text-block.html.twig * field--field-section-title.html.twig * field--string.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <h2 class="section-title" > Using Function Notation</h2> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--default--paragraph--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--default--paragraph--basic-text-block.html.twig * field--default--paragraph--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--default--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--default--basic-text-block.html.twig * field--default--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--default.html.twig * field--theme-ds-field-default.html.twig * field--paragraph--dynamic-token-field--paragraph-paragraph-text-block--basic-text-block.html.twig * field--paragraph--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--paragraph--basic-text-block.html.twig * field--dynamic-token-field--paragraph-paragraph-text-block.html.twig * field--ds.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-dynamic-token-fieldparagraph-paragraph-text-block field--type-ds field--label-hidden field--item"><div class="p-textblock width-default" data-bgcolor="#FFFFFF"><div class="tex2jax_process"><p>Once we determine that a relationship is a function, we need to display and define the functional relationships so that we can understand and use them, and sometimes also so that we can program them into computers. There are various ways of representing functions. A standard function notation is one representation that facilitates working with functions.</p> <p>To represent “height is a function of age,” we start by identifying the descriptive variables \(h\) for height and \(a\) for age. The letters \(f\), \(g\), and \(h\) are often used to represent functions just as we use \(x, y\), and \(z\) to represent numbers and \(A, B\), and \(C\) to represent sets.</p> <p>$$ \begin{array}{lcccc}h\text{ is }f\text{ of }a&&&&\text{We name the function }f;\text{ height is a function of age}.\\h=f(a)&&&&\text{We use parentheses to indicate the function input}\text{. }\\f(a)&&&&\text{We name the function }f;\text{ the expression is read as “}f\text{ of }a\text{.”}\end{array} $$</p> <p>Remember, we can use any letter to name the function; the notation \(h(a)\) shows us that \(h\) depends on \(a\). The value a  a must be put into the function \(h\) to get a result. The parentheses indicate that age is input into the function; they do not indicate multiplication.</p> <p>We can also give an algebraic expression as the input to a function. For example \(f(a+b)\) means "first add <em>a</em> and <em>b</em>, and the result is the input for the function <em>f</em>." The operations must be performed in this order to obtain the correct result.</p> <h3>Function Notation</h3> <p>The notation \(y=f(x)\) defines a function named \(f\). This is read as "\(y is a function of x\)". The letter \(x\) represents the input value, or independent variable. The letter \(y\), or \(f(x)\), represents the output value, or dependent variable.</p> </div></div></div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--paragraph--334.html.twig * ds-1col--paragraph-interactive-content-h5p--default.html.twig * ds-1col--paragraph-interactive-content-h5p-.html.twig * ds-1col--paragraph-default.html.twig * ds-1col--paragraph.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div class="paragraph paragraph--type-interactive-content-h5p- paragraph--view-mode-default ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--expert--paragraph--field-section-title--interactive-content-h5p-.html.twig * field--expert--paragraph--interactive-content-h5p-.html.twig * field--expert--paragraph--field-section-title.html.twig * field--expert--field-section-title--interactive-content-h5p-.html.twig * field--expert--interactive-content-h5p-.html.twig * field--expert--field-section-title.html.twig * field--expert.html.twig * field--ds-field-expert.html.twig * field--paragraph--field-section-title--interactive-content-h5p-.html.twig * field--paragraph--field-section-title.html.twig * field--paragraph--interactive-content-h5p-.html.twig * field--field-section-title.html.twig * field--string.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <h2 class="section-title" > Practice Quiz</h2> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--default--paragraph--field-interactive-content--interactive-content-h5p-.html.twig * field--default--paragraph--interactive-content-h5p-.html.twig * field--default--paragraph--field-interactive-content.html.twig * field--default--field-interactive-content--interactive-content-h5p-.html.twig * field--default--interactive-content-h5p-.html.twig * field--default--field-interactive-content.html.twig * field--default.html.twig * field--theme-ds-field-default.html.twig * field--paragraph--field-interactive-content--interactive-content-h5p-.html.twig * field--paragraph--field-interactive-content.html.twig * field--paragraph--interactive-content-h5p-.html.twig * field--field-interactive-content.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-interactive-content field--type-entity-reference field--label-hidden field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--node--145.html.twig * ds-1col--node-resource-h5p-teaser.html.twig * ds-1col--node-resource-h5p.html.twig * ds-1col--node-teaser.html.twig * ds-1col--node.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div data-history-node-id="145" class="node node--type-resource-h5p node--view-mode-teaser ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--default--node--field-h5p-content--resource-h5p.html.twig * field--default--node--resource-h5p.html.twig * field--default--node--field-h5p-content.html.twig * field--default--field-h5p-content--resource-h5p.html.twig * field--default--resource-h5p.html.twig * field--default--field-h5p-content.html.twig * field--default.html.twig * field--theme-ds-field-default.html.twig * field--node--field-h5p-content--resource-h5p.html.twig * field--node--field-h5p-content.html.twig * field--node--resource-h5p.html.twig * field--field-h5p-content.html.twig * field--h5p.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-h5p-content field--type-h5p field--label-hidden field--item"><div class="h5p-iframe-wrapper"><iframe enable-annotation id="h5p-iframe-24" class="h5p-iframe" data-content-id="24" frameborder="0" scrolling="no"></iframe></div></div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--paragraph--557.html.twig * ds-1col--paragraph-embed-code-default.html.twig * ds-1col--paragraph-embed-code.html.twig * ds-1col--paragraph-default.html.twig * ds-1col--paragraph.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div class="paragraph paragraph--type-embed-code paragraph--view-mode-default ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--default--paragraph--field-embed-code--embed-code.html.twig * field--default--paragraph--embed-code.html.twig * field--default--paragraph--field-embed-code.html.twig * field--default--field-embed-code--embed-code.html.twig * field--default--embed-code.html.twig * field--default--field-embed-code.html.twig * field--default.html.twig * field--theme-ds-field-default.html.twig * field--paragraph--field-embed-code--embed-code.html.twig * field--paragraph--field-embed-code.html.twig * field--paragraph--embed-code.html.twig * field--field-embed-code.html.twig * field--text-long.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-embed-code field--type-text-long field--label-hidden field--item"><iframe src="https://www.geogebra.org/classic/gjencrn6?embed" width="800" height="600" allowfullscreen="" frameborder="0"></iframe></div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_entity_view' --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'ds_1col' --> <!-- FILE NAME SUGGESTIONS: * ds-1col--paragraph--679.html.twig * ds-1col--paragraph-notification-box-default.html.twig * ds-1col--paragraph-notification-box.html.twig * ds-1col--paragraph-default.html.twig * ds-1col--paragraph.html.twig x ds-1col.html.twig x ds-1col.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <div class="paragraph paragraph--type-notification-box paragraph--view-mode-default ds-1col clearfix"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--expert--paragraph--field-text-content--notification-box.html.twig * field--expert--paragraph--notification-box.html.twig * field--expert--paragraph--field-text-content.html.twig * field--expert--field-text-content--notification-box.html.twig * field--expert--notification-box.html.twig * field--expert--field-text-content.html.twig * field--expert.html.twig * field--ds-field-expert.html.twig * field--paragraph--field-text-content--notification-box.html.twig * field--paragraph--field-text-content.html.twig * field--paragraph--notification-box.html.twig * field--field-text-content.html.twig * field--text-long.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> <div class="alert alert-info"> <p>Content for this page has been sourced from OpenStax - Access for free at https://openstax.org/books/algebra-and-trigonometry/pages/1-introduction-to-prerequisites</p> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-field-expert.html.twig' --> </div> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-1col.html.twig' --> <!-- END OUTPUT from 'modules/contrib/ds/templates/ds-entity-view.html.twig' --> </div> </div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-cover-image--resource-tutorial.html.twig * field--node--field-cover-image.html.twig * field--node--resource-tutorial.html.twig * field--field-cover-image.html.twig * field--image.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-cover-image field--type-image field--label-above"> <div class="field--label">Cover Image</div> <div class="field--item"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'image_formatter' --> <!-- BEGIN OUTPUT from 'core/modules/image/templates/image-formatter.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'image' --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/system/image.html.twig' --> <img src="/sites/default/files/up/tutorial/cover-image/2020-07/black-and-white-blur-book-business-240163.jpg" width="1280" height="720" alt="" typeof="foaf:Image" class="img-responsive" /> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/system/image.html.twig' --> <!-- END OUTPUT from 'core/modules/image/templates/image-formatter.html.twig' --> </div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-included-in-feeds--resource-tutorial.html.twig * field--node--field-included-in-feeds.html.twig * field--node--resource-tutorial.html.twig * field--field-included-in-feeds.html.twig * field--boolean.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-included-in-feeds field--type-boolean field--label-above"> <div class="field--label">Share in catalogue</div> <div class="field--item">On</div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-tags--resource-tutorial.html.twig * field--node--field-tags.html.twig * field--node--resource-tutorial.html.twig * field--field-tags.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-tags field--type-entity-reference field--label-above"> <div class="field--label">Tags</div> <div class="field--items"> <div class="field--item"><a href="/taxonomy/term/166" hreflang="en">Math</a></div> <div class="field--item"><a href="/taxonomy/term/167" hreflang="en">Algebra</a></div> <div class="field--item"><a href="/taxonomy/term/168" hreflang="en">Functions</a></div> </div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-top-bar-region-tutorials--resource-tutorial.html.twig * field--node--field-top-bar-region-tutorials.html.twig * field--node--resource-tutorial.html.twig * field--field-top-bar-region-tutorials.html.twig * field--markup.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-top-bar-region-tutorials field--type-markup field--label-above"> <div class="field--label">Top Bar Region - Tutorials</div> <div class="field--item"><div class="col-md-6 hidden-xs hidden-sm" id="top-bar-left"> <div class="btn-group"> <a class="btn btn-primary btn-sm" href="/forum/3/creating-and-sharing-resources" target="_blank">Documentation</a> <!--<a class="btn btn-primary btn-sm" href="#">Help</a>--> </div> </div> <div class="col-md-6 text-right" id="top-bar-right"></div> </div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-creative-commons-license--resource-tutorial.html.twig * field--node--field-creative-commons-license.html.twig * field--node--resource-tutorial.html.twig * field--field-creative-commons-license.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-creative-commons-license field--type-entity-reference field--label-above"> <div class="field--label">Creative Commons License</div> <div class="field--item"><a href="/taxonomy/term/54" hreflang="en">CC BY</a></div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-education-level--resource-tutorial.html.twig * field--node--field-education-level.html.twig * field--node--resource-tutorial.html.twig * field--field-education-level.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-education-level field--type-entity-reference field--label-above"> <div class="field--label">Education Level</div> <div class="field--item"><a href="/taxonomy/term/134" hreflang="en">High School</a></div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-educational-use--resource-tutorial.html.twig * field--node--field-educational-use.html.twig * field--node--resource-tutorial.html.twig * field--field-educational-use.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-educational-use field--type-entity-reference field--label-above"> <div class="field--label">Educational Use</div> <div class="field--item"><a href="/taxonomy/term/109" hreflang="en">Instruction</a></div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-material-type--resource-tutorial.html.twig * field--node--field-material-type.html.twig * field--node--resource-tutorial.html.twig * field--field-material-type.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-material-type field--type-entity-reference field--label-above"> <div class="field--label">Material Type</div> <div class="field--item"><a href="/taxonomy/term/130" hreflang="en">Reading Material</a></div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-subject-area--resource-tutorial.html.twig * field--node--field-subject-area.html.twig * field--node--resource-tutorial.html.twig * field--field-subject-area.html.twig * field--entity-reference.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-subject-area field--type-entity-reference field--label-above"> <div class="field--label">Subject Area</div> <div class="field--item"><a href="/taxonomy/term/149" hreflang="en">Mathematics</a></div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-brief-description--resource-tutorial.html.twig * field--node--field-brief-description.html.twig * field--node--resource-tutorial.html.twig * field--field-brief-description.html.twig * field--string-long.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-brief-description field--type-string-long field--label-above"> <div class="field--label">Brief Description</div> <div class="field--item">A demonstration of the MathJax authoring capabilities. Content for this page has been sourced from OpenStax - Access for free at https://openstax.org/books/algebra-and-trigonometry/pages/1-introduction-to-prerequisites</div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--comment--resource-tutorial.html.twig * field--node--comment.html.twig * field--node--resource-tutorial.html.twig x field--comment.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'themes/custom/learnful-theme/templates/field--comment.html.twig' --> <section id="node-resource-tutorial-comment--5"> <p class="for-guest"><a href="/login">Login</a> or <a href="/signup/beta">register</a> to join the discussion.</p> <div id="comment-list"> <h2>Comments</h2> <p class="text-muted small">Be the first to comment!</p> </div> </section> <!-- END OUTPUT from 'themes/custom/learnful-theme/templates/field--comment.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-report-adaption--resource-tutorial.html.twig * field--node--field-report-adaption.html.twig * field--node--resource-tutorial.html.twig x field--field-report-adaption.html.twig * field--comment.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'themes/custom/learnful-theme/templates/field--field-report-adaption.html.twig' --> <section id="node-resource-tutorial-field-report-adaption--5"> <p class="for-guest"><a href="/login">Login</a> or <a href="/signup/beta">register</a> to share your adaptations.</p> <div id="comment-list"> <h2>List of adaptions</h2> <p class="text-muted small">Be the first to add your adaptation here!</p> </div> </section> <!-- END OUTPUT from 'themes/custom/learnful-theme/templates/field--field-report-adaption.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-top-bar-region-lesson-clon--resource-tutorial.html.twig * field--node--field-top-bar-region-lesson-clon.html.twig * field--node--resource-tutorial.html.twig * field--field-top-bar-region-lesson-clon.html.twig * field--markup.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-top-bar-region-lesson-clon field--type-markup field--label-above"> <div class="field--label">Top Bar Region - Lesson - Clone</div> <div class="field--item"><div class="col-md-6 hidden-xs hidden-sm" id="top-bar-left"> <div class="btn-group"> </div> </div> <div class="col-md-6 text-right" id="top-bar-right"></div></div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-display-in-portfolio--resource-tutorial.html.twig * field--node--field-display-in-portfolio.html.twig * field--node--resource-tutorial.html.twig * field--field-display-in-portfolio.html.twig * field--boolean.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-display-in-portfolio field--type-boolean field--label-above"> <div class="field--label">Display in Portfolio</div> <div class="field--item">Off</div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-license-is-derivative--resource-tutorial.html.twig * field--node--field-license-is-derivative.html.twig * field--node--resource-tutorial.html.twig * field--field-license-is-derivative.html.twig * field--boolean.html.twig x field.html.twig --> <!-- BEGIN OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <div class="field field--name-field-license-is-derivative field--type-boolean field--label-above"> <div class="field--label">This work is a derivative</div> <div class="field--item">Off</div> </div> <!-- END OUTPUT from 'themes/contrib/bootstrap/templates/field/field.html.twig' --> <!-- THEME DEBUG --> <!-- THEME HOOK: 'field' --> <!-- FILE NAME SUGGESTIONS: * field--node--field-feedback-review--resource-tutorial.html.twig * field--node--field-feedback-review.html.twig * field--node--resource-tutorial.html.twig x field--field-feedback-review.html.twig * field--comment.html.twig * field.html.twig --> <!-- BEGIN OUTPUT from 'themes/custom/learnful-theme/templates/field--field-feedback-review.html.twig' --> <section id="node-resource-tutorial-field-feedback-review--5"> <p class="for-guest"><a href="/login">Login</a> or <a href="/signup/beta">register</a> to engage in the review and feedback process.</p> <div id="comment-list"> <h2>Reviews and Feedback</h2> <p class="text-muted small">Be the first to review!</p> </div> </section> <!-- END OUTPUT from 'themes/custom/learnful-theme/templates/field--field-feedback-review.html.twig' --> Fri, 03 Jul 2020 03:37:56 +0000 Help@Learnful 143 at https://learnful.ca https://learnful.ca/lesson/143#comments https://learnful.ca/lesson/143#comments https://learnful.ca/lesson/143#comments