MAT1L Lesson Template

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Learning Objectives

  1. Add learning objectives here
  2. Examples of learning objectives can include:
  3. Understand how to solve for 'x'
  4. Read and create functions
  5. And so on
Photo of a pen on top of paper with math expressions

Swap out this image with an image of your own.

Introduction to the Lesson should go here. You should introduce the topic in one or two paragraphs. 

Praesent nonummy mi in odio. Phasellus magna. In dui magna, posuere eget, vestibulum et, tempor auctor, justo. Nulla neque dolor, sagittis eget, iaculis quis, molestie non, velit.

You can also add mathematical expressions and functions using the LaTex notation. For example the following syntax:

$$\{(1,\text{ }2),\text{ }(2,\text{ }4),\text{ }(3,\text{ }6),\text{ }(4,\text{ }8),\text{ }(5,\text{ }10)\}$$

Produces the following expression:

$$\{(1,\text{ }2),\text{ }(2,\text{ }4),\text{ }(3,\text{ }6),\text{ }(4,\text{ }8),\text{ }(5,\text{ }10)\}$$

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This is a template for creating Lessons.

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Remix of Functions and Function Notation

Content Blocks

Learning Objectives

In this section, you will:

  • Determine whether a relation represents a function.
  • Find the value of a function.
  • Determine whether a function is one-to-one.
  • Use the vertical line test to identify functions.
  • Graph the functions listed in the library of functions.

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.

Determining Whether a Relation Represents a Function

A relation is a set of ordered pairs. The set consisting of the first components of each ordered pair is called the domain and the set consisting of the second components of each ordered pair is called the range. 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.

$$\{(1,\text{ }2),\text{ }(2,\text{ }4),\text{ }(3,\text{ }6),\text{ }(4,\text{ }8),\text{ }(5,\text{ }10)\}$$

The domain is \(\{1,\text{ }2,\text{ }3,\text{ }4,\text{ }5\}\). The range is \(\{2,\text{ }4,\text{ }6,\text{ }8,\text{ }10\}\).

Note that each value in the domain is also known as an input value, or independent variable, and is often labeled with the lowercase letter \(x\). Each value in the range is also known as an output value, or dependent variable, and is often labeled lowercase letter \(y\).

A function \(f\) is a relation that assigns a single value in the range to each value in the domain. In other words, no x-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, \(\{2, 4, 6, 8, 10\}\).

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

$$\{{(\text{odd},\text{ }1),\text{ }(\text{even},\text{ }2),\text{ }(\text{odd},\text{ }3),\text{ }(\text{even},\text{ }4),\text{ }(\text{odd},\text{ }5)}\}$$

Notice that each element in the domain, \(\{even, odd\}\) is not 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.

Figure 1 compares relations that are functions and not functions.

Three relations that demonstrate what constitute a function.

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.

Functions

function 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.”

The input values make up the domain, and the output values make up the range.

Examples

Given a relationship between two quantities, determine whether the relationship is a function.

Using Function Notation

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.

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.

$$ \begin{array}{lcccc}h\text{ is }f\text{ of }a&&&&\text{We name the function }f;\text{ height is a function of age}.\\h=f(a)&&&&\text{We use parentheses to indicate the function input}\text{. }\\f(a)&&&&\text{We name the function }f;\text{ the expression is read as “}f\text{ of }a\text{.”}\end{array} $$

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.

We can also give an algebraic expression as the input to a function. For example \(f(a+b)\) means "first add a and b, and the result is the input for the function f." The operations must be performed in this order to obtain the correct result.

Function Notation

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.

Practice Quiz

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

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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

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Daring Dragon - Remix of Indigenous Vocabulary: Algonquin Words

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Statue of Keewakwa Abenaki Keenahbeh in Opechee Park in Laconia, New Hampshire (standing at 36 ft.)

Statue of Keewakwa Abenaki Keenahbeh in Opechee Park in Laconia, New Hampshire (standing at 36 ft.). Sources: Sculptor: Peter Wolf Toth / Photo by: Niranjan Arminius - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=51375010

The Abenaki (Abnaki, Abinaki, Alnôbak) are a Native American tribe and First Nation. They are one of the Algonquian-speaking peoples of northeastern North America. The Abenaki originated in a region called Wabanahkik in the Eastern Algonquian languages (meaning "Dawn Land"), a territory now including parts of Quebec and the Maritimes of Canada and northern sections of the New England region of the United States. The Abenaki are one of the five members of the Wabanaki Confederacy.

The Abenaki language is closely related to the Panawahpskek (Penobscot) language. Other neighboring Wabanaki tribes, the Pestomuhkati (Passamaquoddy), Wolastoqiyik (Maliseet), and Miꞌkmaq, and other Eastern Algonquian languages share many linguistic similarities. It has come close to extinction as a spoken language. Tribal members are working to revive the Abenaki language at Odanak (means "in the village"), a First Nations Abenaki reserve near Pierreville, Quebec, and throughout New Hampshire, Vermont and New York state.

Twenty Basic Words in Algonquin

Abenaki is an Algonquian language, related to other languages like Lenape and Ojibwe. We have included twenty basic Algonquin words here.

Algonquin Word Set

English (Français) Algonquin Words
One (Un) Pejig
Two (Deux) Nìj
Three (Trois) Niswi
Four (Quatre) New
Five (Cinq) Nànan
Man (Homme) Ininì
Woman (Femme) Ikwe
Dog (Chien) Animosh
Sun (Soleil) Kìzis
Moon (Lune) Tibik-kìzis
Water (Eau) Nibì
White (Blanc) Wàbà
Yellow (Jaune) Ozàwà
Red (Rouge) Miskwà
Black (Noir) Makadewà
Eat (Manger) Mìdjin
See (Voir) Wàbi
Hear (Entendre) Nòndam
Sing (Chanter) Nigamo
Leave (Partir) Màdjà or Nagadàn

Test your memory

Please note: the content on this page, sourced from http://www.native-languages.org/algonquin_words.htm, is meant for demonstration purposes only.

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Abenaki is an Algonquian language, related to other languages like Lenape and Ojibwe. We have included twenty basic Algonquin words here.

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Remix (Test) of Indigenous Vocabulary: Algonquin Words

Content Blocks
Statue of Keewakwa Abenaki Keenahbeh in Opechee Park in Laconia, New Hampshire (standing at 36 ft.)

Statue of Keewakwa Abenaki Keenahbeh in Opechee Park in Laconia, New Hampshire (standing at 36 ft.). Sources: Sculptor: Peter Wolf Toth / Photo by: Niranjan Arminius - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=51375010

The Abenaki (Abnaki, Abinaki, Alnôbak) are a Native American tribe and First Nation. They are one of the Algonquian-speaking peoples of northeastern North America. The Abenaki originated in a region called Wabanahkik in the Eastern Algonquian languages (meaning "Dawn Land"), a territory now including parts of Quebec and the Maritimes of Canada and northern sections of the New England region of the United States. The Abenaki are one of the five members of the Wabanaki Confederacy.

The Abenaki language is closely related to the Panawahpskek (Penobscot) language. Other neighboring Wabanaki tribes, the Pestomuhkati (Passamaquoddy), Wolastoqiyik (Maliseet), and Miꞌkmaq, and other Eastern Algonquian languages share many linguistic similarities. It has come close to extinction as a spoken language. Tribal members are working to revive the Abenaki language at Odanak (means "in the village"), a First Nations Abenaki reserve near Pierreville, Quebec, and throughout New Hampshire, Vermont and New York state.

Twenty Basic Words in Algonquin

Abenaki is an Algonquian language, related to other languages like Lenape and Ojibwe. We have included twenty basic Algonquin words here.

Algonquin Word Set

English (Français) Algonquin Words
One (Un) Pejig
Two (Deux) Nìj
Three (Trois) Niswi
Four (Quatre) New
Five (Cinq) Nànan
Man (Homme) Ininì
Woman (Femme) Ikwe
Dog (Chien) Animosh
Sun (Soleil) Kìzis
Moon (Lune) Tibik-kìzis
Water (Eau) Nibì
White (Blanc) Wàbà
Yellow (Jaune) Ozàwà
Red (Rouge) Miskwà
Black (Noir) Makadewà
Eat (Manger) Mìdjin
See (Voir) Wàbi
Hear (Entendre) Nòndam
Sing (Chanter) Nigamo
Leave (Partir) Màdjà or Nagadàn

Please note: the content on this page, sourced from http://www.native-languages.org/algonquin_words.htm, is meant for demonstration purposes only.

Test your memory

Assessment

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Abenaki is an Algonquian language, related to other languages like Lenape and Ojibwe. We have included twenty basic Algonquin words here.

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My Remix of Functions and Function Notation

Content Blocks

Learning Objectives

In this section, you will:

  • Determine whether a relation represents a function.
  • Find the value of a function.
  • Determine whether a function is one-to-one.
  • Use the vertical line test to identify functions.
  • Graph the functions listed in the library of functions.

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.

Determining Whether a Relation Represents a Function

A relation is a set of ordered pairs. The set consisting of the first components of each ordered pair is called the domain and the set consisting of the second components of each ordered pair is called the range. 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.

$$\{(1,\text{ }2),\text{ }(2,\text{ }4),\text{ }(3,\text{ }6),\text{ }(4,\text{ }8),\text{ }(5,\text{ }10)\}$$

The domain is \(\{1,\text{ }2,\text{ }3,\text{ }4,\text{ }5\}\). The range is \(\{2,\text{ }4,\text{ }6,\text{ }8,\text{ }10\}\).

Note that each value in the domain is also known as an input value, or independent variable, and is often labeled with the lowercase letter \(x\). Each value in the range is also known as an output value, or dependent variable, and is often labeled lowercase letter \(y\).

A function \(f\) is a relation that assigns a single value in the range to each value in the domain. In other words, no x-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, \(\{2, 4, 6, 8, 10\}\).

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

$$\{{(\text{odd},\text{ }1),\text{ }(\text{even},\text{ }2),\text{ }(\text{odd},\text{ }3),\text{ }(\text{even},\text{ }4),\text{ }(\text{odd},\text{ }5)}\}$$

Notice that each element in the domain, \(\{even, odd\}\) is not 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.

Figure 1 compares relations that are functions and not functions.

Three relations that demonstrate what constitute a function.

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.

Functions

function 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.”

The input values make up the domain, and the output values make up the range.

Examples

Given a relationship between two quantities, determine whether the relationship is a function.

Using Function Notation

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.

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.

$$ \begin{array}{lcccc}h\text{ is }f\text{ of }a&&&&\text{We name the function }f;\text{ height is a function of age}.\\h=f(a)&&&&\text{We use parentheses to indicate the function input}\text{. }\\f(a)&&&&\text{We name the function }f;\text{ the expression is read as “}f\text{ of }a\text{.”}\end{array} $$

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.

We can also give an algebraic expression as the input to a function. For example \(f(a+b)\) means "first add a and b, and the result is the input for the function f." The operations must be performed in this order to obtain the correct result.

Function Notation

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.

Practice Quiz

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

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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

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Anatomy & Physiology

Instructional Summary
This is an example of a Module resource. Modules are comprised of lessons and h5p resources. Resources are added to the Module's Table of Contents to create a bundled resource.

The content on this page/module is for demonstration purposes only. You can view the original work here: https://training.seer.cancer.gov/anatomy/
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<span>Photo by <a href="https://unsplash.com/@pierreacobas?utm_source=unsplash&amp;utm_medium=referral&amp;utm_content=creditCopyText">Pierre Acobas</a> on <a href="https://unsplash.com/s/photos/anatomy?utm_source=unsplash&amp;utm_medium=referral&amp;utm_content=creditCopyText">Unsplash</a></span>
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Introduction

The Anatomy and Physiology module introduces the structure and function of the human body. You will read about the cells, tissues and membranes that make up our bodies and how our major systems function to help us develop and stay healthy.

In this module you will learn to:

  • Describe basic human body functions and life process.
  • Name the major human body systems and relate their functions.
  • Describe the anatomical locations, structures and physiological functions of the main components of each major system of the human body.
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Remix of Functions and Function Notation

Content Blocks

Learning Objectives

In this section, you will:

  • Determine whether a relation represents a function.
  • Find the value of a function.
  • Determine whether a function is one-to-one.
  • Use the vertical line test to identify functions.
  • Graph the functions listed in the library of functions.

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.

Determining Whether a Relation Represents a Function

A relation is a set of ordered pairs. The set consisting of the first components of each ordered pair is called the domain and the set consisting of the second components of each ordered pair is called the range. 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.

$$\{(1,\text{ }2),\text{ }(2,\text{ }4),\text{ }(3,\text{ }6),\text{ }(4,\text{ }8),\text{ }(5,\text{ }10)\}$$

The domain is \(\{1,\text{ }2,\text{ }3,\text{ }4,\text{ }5\}\). The range is \(\{2,\text{ }4,\text{ }6,\text{ }8,\text{ }10\}\).

Note that each value in the domain is also known as an input value, or independent variable, and is often labeled with the lowercase letter \(x\). Each value in the range is also known as an output value, or dependent variable, and is often labeled lowercase letter \(y\).

A function \(f\) is a relation that assigns a single value in the range to each value in the domain. In other words, no x-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, \(\{2, 4, 6, 8, 10\}\).

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

$$\{{(\text{odd},\text{ }1),\text{ }(\text{even},\text{ }2),\text{ }(\text{odd},\text{ }3),\text{ }(\text{even},\text{ }4),\text{ }(\text{odd},\text{ }5)}\}$$

Notice that each element in the domain, \(\{even, odd\}\) is not 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.

Figure 1 compares relations that are functions and not functions.

Three relations that demonstrate what constitute a function.

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.

Functions

function 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.”

The input values make up the domain, and the output values make up the range.

Examples

Given a relationship between two quantities, determine whether the relationship is a function.

Using Function Notation

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.

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.

$$ \begin{array}{lcccc}h\text{ is }f\text{ of }a&&&&\text{We name the function }f;\text{ height is a function of age}.\\h=f(a)&&&&\text{We use parentheses to indicate the function input}\text{. }\\f(a)&&&&\text{We name the function }f;\text{ the expression is read as “}f\text{ of }a\text{.”}\end{array} $$

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.

We can also give an algebraic expression as the input to a function. For example \(f(a+b)\) means "first add a and b, and the result is the input for the function f." The operations must be performed in this order to obtain the correct result.

Function Notation

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.

Practice Quiz

Content for this page has been sourced from OpenStax - Access for free at https://openstax.org/books/algebra-and-trigonometry/pages/1-introductio…

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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

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Indigenous Vocabulary: Algonquin Words

Content Blocks
Statue of Keewakwa Abenaki Keenahbeh in Opechee Park in Laconia, New Hampshire (standing at 36 ft.)

Statue of Keewakwa Abenaki Keenahbeh in Opechee Park in Laconia, New Hampshire (standing at 36 ft.). Sources: Sculptor: Peter Wolf Toth / Photo by: Niranjan Arminius - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=51375010

The Abenaki (Abnaki, Abinaki, Alnôbak) are a Native American tribe and First Nation. They are one of the Algonquian-speaking peoples of northeastern North America. The Abenaki originated in a region called Wabanahkik in the Eastern Algonquian languages (meaning "Dawn Land"), a territory now including parts of Quebec and the Maritimes of Canada and northern sections of the New England region of the United States. The Abenaki are one of the five members of the Wabanaki Confederacy.

The Abenaki language is closely related to the Panawahpskek (Penobscot) language. Other neighboring Wabanaki tribes, the Pestomuhkati (Passamaquoddy), Wolastoqiyik (Maliseet), and Miꞌkmaq, and other Eastern Algonquian languages share many linguistic similarities. It has come close to extinction as a spoken language. Tribal members are working to revive the Abenaki language at Odanak (means "in the village"), a First Nations Abenaki reserve near Pierreville, Quebec, and throughout New Hampshire, Vermont and New York state.

Twenty Basic Words in Algonquin

Abenaki is an Algonquian language, related to other languages like Lenape and Ojibwe. We have included twenty basic Algonquin words here.

Algonquin Word Set

English (Français) Algonquin Words
One (Un) Pejig
Two (Deux) Nìj
Three (Trois) Niswi
Four (Quatre) New
Five (Cinq) Nànan
Man (Homme) Ininì
Woman (Femme) Ikwe
Dog (Chien) Animosh
Sun (Soleil) Kìzis
Moon (Lune) Tibik-kìzis
Water (Eau) Nibì
White (Blanc) Wàbà
Yellow (Jaune) Ozàwà
Red (Rouge) Miskwà
Black (Noir) Makadewà
Eat (Manger) Mìdjin
See (Voir) Wàbi
Hear (Entendre) Nòndam
Sing (Chanter) Nigamo
Leave (Partir) Màdjà or Nagadàn

Test your memory

Please note: the content on this page, sourced from http://www.native-languages.org/algonquin_words.htm, is meant for demonstration purposes only.

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Abenaki is an Algonquian language, related to other languages like Lenape and Ojibwe. We have included twenty basic Algonquin words here.

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Functions and Function Notation

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Learning Objectives

In this section, you will:

  • Determine whether a relation represents a function.
  • Find the value of a function.
  • Determine whether a function is one-to-one.
  • Use the vertical line test to identify functions.
  • Graph the functions listed in the library of functions.

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.

Determining Whether a Relation Represents a Function

A relation is a set of ordered pairs. The set consisting of the first components of each ordered pair is called the domain and the set consisting of the second components of each ordered pair is called the range. 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.

$$\{(1,\text{ }2),\text{ }(2,\text{ }4),\text{ }(3,\text{ }6),\text{ }(4,\text{ }8),\text{ }(5,\text{ }10)\}$$

The domain is \(\{1,\text{ }2,\text{ }3,\text{ }4,\text{ }5\}\). The range is \(\{2,\text{ }4,\text{ }6,\text{ }8,\text{ }10\}\).

Note that each value in the domain is also known as an input value, or independent variable, and is often labeled with the lowercase letter \(x\). Each value in the range is also known as an output value, or dependent variable, and is often labeled lowercase letter \(y\).

A function \(f\) is a relation that assigns a single value in the range to each value in the domain. In other words, no x-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, \(\{2, 4, 6, 8, 10\}\).

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

$$\{{(\text{odd},\text{ }1),\text{ }(\text{even},\text{ }2),\text{ }(\text{odd},\text{ }3),\text{ }(\text{even},\text{ }4),\text{ }(\text{odd},\text{ }5)}\}$$

Notice that each element in the domain, \(\{even, odd\}\) is not 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.

Figure 1 compares relations that are functions and not functions.

Three relations that demonstrate what constitute a function.

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.

Functions

function 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.”

The input values make up the domain, and the output values make up the range.

Examples

Given a relationship between two quantities, determine whether the relationship is a function.

Using Function Notation

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.

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.

$$ \begin{array}{lcccc}h\text{ is }f\text{ of }a&&&&\text{We name the function }f;\text{ height is a function of age}.\\h=f(a)&&&&\text{We use parentheses to indicate the function input}\text{. }\\f(a)&&&&\text{We name the function }f;\text{ the expression is read as “}f\text{ of }a\text{.”}\end{array} $$

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.

We can also give an algebraic expression as the input to a function. For example \(f(a+b)\) means "first add a and b, and the result is the input for the function f." The operations must be performed in this order to obtain the correct result.

Function Notation

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.

Practice Quiz

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

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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

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Introduction to HTML

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Photo of person using a laptop to write CSS code.

Photo of person using a laptop to write CSS code. Photo credit: Lukas from https://www.pexels.com/@goumbik

Introduction

HTML is the standard markup language for creating Web pages.

What is HTML?

  • HTML stands for Hyper Text Markup Language
  • HTML is the standard markup language for creating Web pages
  • HTML describes the structure of a Web page
  • HTML consists of a series of elements
  • HTML elements tell the browser how to display the content

HTML elements label pieces of content such as "this is a heading", "this is a paragraph", "this is a link", etc.

Sir Tim Berners Lee arriving at the Guildhall to receive the Honorary Freedom of the City of London.

Sir Tim Berners Lee arriving at the Guildhall to receive the Honorary Freedom of the City of London. Photo credit: Paul Clark https://www.wikidata.org/wiki/Q20202034

Tim Berners-Lee

In 1980, physicist Tim Berners-Lee, a contractor at CERN, proposed a system for CERN researchers to use and share documents. In 1989, Berners-Lee wrote a memo proposing an Internet-based hypertext system. Berners-Lee specified HTML and wrote the browser and server software in late 1990. The first publicly available description of HTML was a document called "HTML Tags", first mentioned on the Internet by Tim Berners-Lee in late 1991. It describes 18 elements comprising the initial, relatively simple design of HTML. Except for the hyperlink tag, these were strongly influenced by SGMLguid, an in-house Standard Generalized Markup Language (SGML)-based documentation format at CERN. Eleven of these elements still exist in HTML 4.

Source: https://en.wikipedia.org/wiki/HTML

A Simple HTML Document 




Page Title



My First Heading

My first paragraph.

Example Explained

  • The declaration defines that this document is an HTML5 document
  • The element is the root element of an HTML page
  • The element contains meta information about the HTML page
  • The element specifies a title for the HTML page (which is shown in the browser's title bar or in the page's tab)</li> <li>The <body> element defines the document's body, and is a container for all the visible contents, such as headings, paragraphs, images, hyperlinks, tables, lists, etc.</li> <li>The <h1> element defines a large heading</li> <li>The <p> element defines a paragraph</li> </ul> </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--253.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>What is an HTML Element?</h2> <p>An HTML element is defined by a start tag, some content, and an end tag:</p> <pre> <code class="language-twig"><tagname>Content goes here...</tagname></code></pre><p>The HTML element is everything from the start tag to the end tag:</p> <pre> <code class="language-twig"><h1>My First Heading</h1> <p>My first paragraph.</p></code></pre><table> <tbody> <tr> <td> <p><strong>Start tag</strong></p> </td> <td> <p><strong>Element content</strong></p> </td> <td> <p><strong>End tag</strong></p> </td> </tr> <tr> <td> <p><strong><h1></strong></p> </td> <td> <p>My First Heading</p> </td> <td> <p></h1></p> </td> </tr> <tr> <td> <p><strong><p></strong></p> </td> <td> <p>My first paragraph.</p> </td> <td> <p></p></p> </td> </tr> <tr> <td> <p><strong><br></strong></p> </td> <td> <p>none</p> </td> <td> <p>none</p> </td> </tr> </tbody> </table> </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--255.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="#FFDC00"><div class="tex2jax_process"><p><strong>Note: </strong>Some HTML elements have no content (like the <br> element). These elements are called empty elements. Empty elements do not have an end tag!</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--256.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>Web Browsers</h2> <p>The purpose of a web browser (Chrome, Edge, Firefox, Safari) is to read HTML documents and display them correctly.</p> <p>A browser does not display the HTML tags, but uses them to determine how to display the document:</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--257.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="default"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'colorbox_formatter' --> <!-- BEGIN OUTPUT from 'modules/contrib/colorbox/templates/colorbox-formatter.html.twig' --> <a href="https://www.learnful.ca/sites/default/files/up/para/field-image/2020-06/78/webbrowser_0.png" title="Screenshot of a web browser displaying a basic html webpage." data-colorbox-gallery="" class="colorbox" data-cbox-img-attrs="{"alt":"Screenshot of a web browser displaying a basic html webpage."}"> <!-- 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/2020-06/78/webbrowser_0.png?itok=6V_HbRji" width="1400" height="796" alt="Screenshot of a web browser displaying a basic html webpage." 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="default"> <div class="tex2jax_process"><p>Screenshot of a web browser displaying a basic html webpage.</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--258.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>HTML Page Structure</h2> <p>Below is a visualization of an HTML page structure:</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--259.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="default"> <!-- THEME DEBUG --> <!-- THEME HOOK: 'colorbox_formatter' --> <!-- BEGIN OUTPUT from 'modules/contrib/colorbox/templates/colorbox-formatter.html.twig' --> <a href="https://www.learnful.ca/sites/default/files/up/para/field-image/2020-06/78/htmllayout_0.png" title="" data-colorbox-gallery="" class="colorbox" data-cbox-img-attrs="{"alt":"Illustration of a basic html webpage layout."}"> <!-- 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/2020-06/78/htmllayout_0.png?itok=-qTEe4Ie" width="1400" height="948" alt="Illustration of a basic html webpage layout." 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' --> </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--260.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>HTML History</h2> <p>Since the early days of the World Wide Web, there have been many versions of HTML:</p> <table> <tbody> <tr> <td> <p><strong>Year</strong></p> </td> <td> <p><strong>Version</strong></p> </td> </tr> <tr> <td> <p>1989</p> </td> <td> <p>Tim Berners-Lee invented www</p> </td> </tr> <tr> <td> <p>1991</p> </td> <td> <p>Tim Berners-Lee invented HTML</p> </td> </tr> <tr> <td> <p>1993</p> </td> <td> <p>Dave Raggett drafted HTML+</p> </td> </tr> <tr> <td> <p>1995</p> </td> <td> <p>HTML Working Group defined HTML 2.0</p> </td> </tr> <tr> <td> <p>1997</p> </td> <td> <p>W3C Recommendation: HTML 3.2</p> </td> </tr> <tr> <td> <p>1999</p> </td> <td> <p>W3C Recommendation: HTML 4.01</p> </td> </tr> <tr> <td> <p>2000</p> </td> <td> <p>W3C Recommendation: XHTML 1.0</p> </td> </tr> <tr> <td> <p>2008</p> </td> <td> <p>WHATWG HTML5 First Public Draft</p> </td> </tr> <tr> <td> <p>2012</p> </td> <td> <p><a href="http://whatwg.org/html/" rel="nofollow">WHATWG HTML5 Living Standard</a></p> </td> </tr> <tr> <td> <p>2014</p> </td> <td> <p><a href="http://www.w3.org/TR/html5/" rel="nofollow">W3C Recommendation: HTML5</a></p> </td> </tr> <tr> <td> <p>2016</p> </td> <td> <p>W3C Candidate Recommendation: HTML 5.1</p> </td> </tr> <tr> <td> <p>2017</p> </td> <td> <p><a href="http://www.w3.org/TR/html51/" rel="nofollow">W3C Recommendation: HTML5.1 2nd Edition</a></p> </td> </tr> <tr> <td> <p>2017</p> </td> <td> <p><a href="http://www.w3.org/TR/html52/" rel="nofollow">W3C Recommendation: HTML5.2</a></p> </td> </tr> </tbody> </table> </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--262.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>Quiz time!</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--261.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 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/2020-06/coverimage_0.jpg" width="3397" height="2250" 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-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/136" hreflang="en">Undergraduate</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/143" hreflang="en">Career and Technical Education</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 very basic tutorial on HTML to showcase the features of the Content Block editor!</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 * 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Let\\u2019s begin by considering the input as the items on the menu. The output values are then the prices. See Figure B.\u003C\\\/p\u003E\\n\u0022},\u0022subContentId\u0022:\u0022ab8013f0-6c83-431e-b5d5-05e4a66227f2\u0022,\u0022metadata\u0022:{\u0022contentType\u0022:\u0022Text\u0022,\u0022license\u0022:\u0022U\u0022,\u0022title\u0022:\u0022Untitled Text\u0022}},\u0022alwaysDisplayComments\u0022:false,\u0022backgroundOpacity\u0022:0,\u0022displayAsButton\u0022:false,\u0022buttonSize\u0022:\u0022big\u0022,\u0022goToSlideType\u0022:\u0022specified\u0022,\u0022invisible\u0022:false,\u0022solution\u0022:\u0022\u0022},{\u0022x\u0022:5.446623093681917,\u0022y\u0022:6.607929515418502,\u0022width\u0022:39.97821350762527,\u0022height\u0022:5.286343612334802,\u0022action\u0022:{\u0022library\u0022:\u0022H5P.AdvancedText 1.1\u0022,\u0022params\u0022:{\u0022text\u0022:\u0022\u003Cp\u003E\u003Cspan style=\\\u0022color:#999999;\\\u0022\u003E\u003Cstrong\u003EEXAMPLE 1 SOLUTION\u003C\\\/strong\u003E\u003C\\\/span\u003E\u003C\\\/p\u003E\\n\u0022},\u0022subContentId\u0022:\u00223831baa0-77c2-4719-8c53-a1384350adbb\u0022,\u0022metadata\u0022:{\u0022contentType\u0022:\u0022Text\u0022,\u0022license\u0022:\u0022U\u0022,\u0022title\u0022:\u0022Untitled Text\u0022}},\u0022alwaysDisplayComments\u0022:false,\u0022backgroundOpacity\u0022:0,\u0022displayAsButton\u0022:false,\u0022buttonSize\u0022:\u0022big\u0022,\u0022goToSlideType\u0022:\u0022specified\u0022,\u0022invisible\u0022:false,\u0022solution\u0022:\u0022\u0022},{\u0022x\u0022:5.446623093681917,\u0022y\u0022:37.5079295154185,\u0022width\u0022:37.03703703703704,\u0022height\u0022:57.268722466960355,\u0022action\u0022:{\u0022library\u0022:\u0022H5P.AdvancedText 1.1\u0022,\u0022params\u0022:{\u0022text\u0022:\u0022\u003Cp id=\\\u0022fs-id1165135532324\\\u0022\u003Eb. Each item on the menu has only one price, so the price is a function of the item.\u003C\\\/p\u003E\\n\\n\u003Cp\u003ETwo items on the menu have the same price. If we consider the prices to be the input values and the items to be the output, then the same input value could have more than one output associated with it. See Figure C.\u003C\\\/p\u003E\\n\\n\u003Cp\u003ETherefore, the item is a not a function of price.\u003C\\\/p\u003E\\n\u0022},\u0022subContentId\u0022:\u0022cacc2b60-4955-4f03-a8de-b9040d635d05\u0022,\u0022metadata\u0022:{\u0022contentType\u0022:\u0022Text\u0022,\u0022license\u0022:\u0022U\u0022,\u0022title\u0022:\u0022Untitled Text\u0022}},\u0022alwaysDisplayComments\u0022:false,\u0022backgroundOpacity\u0022:0,\u0022displayAsButton\u0022:false,\u0022buttonSize\u0022:\u0022big\u0022,\u0022goToSlideType\u0022:\u0022specified\u0022,\u0022invisible\u0022:false,\u0022solution\u0022:\u0022\u0022},{\u0022x\u0022:56.64488017429194,\u0022y\u0022:90.30837004405286,\u0022width\u0022:39.97821350762527,\u0022height\u0022:5.506607929515418,\u0022action\u0022:{\u0022library\u0022:\u0022H5P.AdvancedText 1.1\u0022,\u0022params\u0022:{\u0022text\u0022:\u0022\u003Cp\u003E\u003Cem\u003EFigure 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Text\u0022}},\u0022alwaysDisplayComments\u0022:false,\u0022backgroundOpacity\u0022:0,\u0022displayAsButton\u0022:false,\u0022buttonSize\u0022:\u0022big\u0022,\u0022goToSlideType\u0022:\u0022specified\u0022,\u0022invisible\u0022:false,\u0022solution\u0022:\u0022\u0022},{\u0022x\u0022:5.446623093681917,\u0022y\u0022:17.662444933920703,\u0022width\u0022:86.05664488017429,\u0022height\u0022:8.810572687224669,\u0022action\u0022:{\u0022library\u0022:\u0022H5P.AdvancedText 1.1\u0022,\u0022params\u0022:{\u0022text\u0022:\u0022\u003Ch3 data-type=\\\u0022title\\\u0022 id=\\\u002294202\\\u0022\u003E\u003Cstrong\u003EDetermining If Class Grade Rules Are Functions\u003C\\\/strong\u003E\u003C\\\/h3\u003E\\n\\n\u003Col id=\\\u0022fs-id1165137646341\\\u0022 type=\\\u0022a\\\u0022\u003E\\n\u003C\\\/ol\u003E\\n\u0022},\u0022subContentId\u0022:\u00221bdf6801-30ab-42a0-86b4-cfe6dbb9bbae\u0022,\u0022metadata\u0022:{\u0022contentType\u0022:\u0022Text\u0022,\u0022license\u0022:\u0022U\u0022,\u0022title\u0022:\u0022Untitled Text\u0022}},\u0022alwaysDisplayComments\u0022:false,\u0022backgroundOpacity\u0022:0,\u0022displayAsButton\u0022:false,\u0022buttonSize\u0022:\u0022big\u0022,\u0022goToSlideType\u0022:\u0022specified\u0022,\u0022invisible\u0022:false,\u0022solution\u0022:\u0022\u0022},{\u0022x\u0022:5.446623093681917,\u0022y\u0022:70.48458149779735,\u0022width\u0022:39.97821350762527,\u0022height\u0022:5.506607929515418,\u0022action\u0022:{\u0022library\u0022:\u0022H5P.AdvancedText 1.1\u0022,\u0022params\u0022:{\u0022text\u0022:\u0022\u003Cp\u003E\u003Cem\u003ETable A\u003C\\\/em\u003E\u003C\\\/p\u003E\\n\u0022},\u0022subContentId\u0022:\u00226e96035e-7994-403c-beca-955fc74af81e\u0022,\u0022metadata\u0022:{\u0022contentType\u0022:\u0022Text\u0022,\u0022license\u0022:\u0022U\u0022,\u0022title\u0022:\u0022Untitled Text\u0022}},\u0022alwaysDisplayComments\u0022:false,\u0022backgroundOpacity\u0022:0,\u0022displayAsButton\u0022:false,\u0022buttonSize\u0022:\u0022big\u0022,\u0022goToSlideType\u0022:\u0022specified\u0022,\u0022invisible\u0022:false,\u0022solution\u0022:\u0022\u0022},{\u0022x\u0022:5.446623093681917,\u0022y\u0022:30.93920704845815,\u0022width\u0022:88.23529411764706,\u0022height\u0022:15.418502202643172,\u0022action\u0022:{\u0022library\u0022:\u0022H5P.AdvancedText 1.1\u0022,\u0022params\u0022:{\u0022text\u0022:\u0022\u003Cp\u003EIn a particular math class, the overall percent grade corresponds to a grade point average. Is grade point average a function of the percent grade? Is the percent grade a function of the grade point average?\u0026nbsp;Table A shows a possible rule for assigning grade points.\u003C\\\/p\u003E\\n\u0022},\u0022subContentId\u0022:\u0022ab8013f0-6c83-431e-b5d5-05e4a66227f2\u0022,\u0022metadata\u0022:{\u0022contentType\u0022:\u0022Text\u0022,\u0022license\u0022:\u0022U\u0022,\u0022title\u0022:\u0022Untitled Text\u0022}},\u0022alwaysDisplayComments\u0022:false,\u0022backgroundOpacity\u0022:0,\u0022displayAsButton\u0022:false,\u0022buttonSize\u0022:\u0022big\u0022,\u0022goToSlideType\u0022:\u0022specified\u0022,\u0022invisible\u0022:false,\u0022solution\u0022:\u0022\u0022},{\u0022x\u0022:5.446623093681917,\u0022y\u0022:6.607929515418502,\u0022width\u0022:39.97821350762527,\u0022height\u0022:5.286343612334802,\u0022action\u0022:{\u0022library\u0022:\u0022H5P.AdvancedText 1.1\u0022,\u0022params\u0022:{\u0022text\u0022:\u0022\u003Cp\u003E\u003Cspan style=\\\u0022color:#999999;\\\u0022\u003E\u003Cstrong\u003EEXAMPLE 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Solution\u0022},{\u0022x\u0022:5.446623093681917,\u0022y\u0022:55.25484581497797,\u0022width\u0022:87.14596949891067,\u0022height\u0022:13.215859030837004,\u0022action\u0022:{\u0022library\u0022:\u0022H5P.Table 1.1\u0022,\u0022params\u0022:{\u0022text\u0022:\u0022\u003Ctable data-id=\\\u0022Table_01_01_01\\\u0022 summary=\\\u0022Table 1 \\\u0022\u003E\\n\\t\u003Ctbody\u003E\\n\\t\\t\u003Ctr\u003E\\n\\t\\t\\t\u003Ctd data-align=\\\u0022center\\\u0022\u003E\u003Cstrong\u003EPercent grade\u003C\\\/strong\u003E\u003C\\\/td\u003E\\n\\t\\t\\t\u003Ctd data-align=\\\u0022center\\\u0022\u003E0\\u201356\u003C\\\/td\u003E\\n\\t\\t\\t\u003Ctd data-align=\\\u0022center\\\u0022\u003E57\\u201361\u003C\\\/td\u003E\\n\\t\\t\\t\u003Ctd data-align=\\\u0022center\\\u0022\u003E62\\u201366\u003C\\\/td\u003E\\n\\t\\t\\t\u003Ctd data-align=\\\u0022center\\\u0022\u003E67\\u201371\u003C\\\/td\u003E\\n\\t\\t\\t\u003Ctd data-align=\\\u0022center\\\u0022\u003E72\\u201377\u003C\\\/td\u003E\\n\\t\\t\\t\u003Ctd 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1.1\u0022,\u0022params\u0022:{\u0022text\u0022:\u0022\u003Cp id=\\\u0022fs-id1165135260743\\\u0022\u003EFor any percent grade earned, there is an associated grade point average, so the grade point average is a function of the percent grade. In other words, if we input the percent grade, the output is a specific grade point average.\u003C\\\/p\u003E\\n\\n\u003Cp id=\\\u0022fs-id1165137807321\\\u0022\u003EIn the grading system given, there is a range of percent grades that correspond to the same grade point average. For example, students who receive a grade point average of 3.0 could have a variety of percent grades ranging from 78 all the way to 86. Thus, percent grade is not a function of grade point average.\u003C\\\/p\u003E\\n\u0022},\u0022subContentId\u0022:\u0022ab8013f0-6c83-431e-b5d5-05e4a66227f2\u0022,\u0022metadata\u0022:{\u0022contentType\u0022:\u0022Text\u0022,\u0022license\u0022:\u0022U\u0022,\u0022title\u0022:\u0022Untitled Text\u0022}},\u0022alwaysDisplayComments\u0022:false,\u0022backgroundOpacity\u0022:0,\u0022displayAsButton\u0022:false,\u0022buttonSize\u0022:\u0022big\u0022,\u0022goToSlideType\u0022:\u0022specified\u0022,\u0022invisible\u0022:false,\u0022solution\u0022:\u0022\u0022},{\u0022x\u0022:5.446623093681917,\u0022y\u0022:6.607929515418502,\u0022width\u0022:39.97821350762527,\u0022height\u0022:5.286343612334802,\u0022action\u0022:{\u0022library\u0022:\u0022H5P.AdvancedText 1.1\u0022,\u0022params\u0022:{\u0022text\u0022:\u0022\u003Cp\u003E\u003Cspan style=\\\u0022color:#999999;\\\u0022\u003E\u003Cstrong\u003EEXAMPLE 2 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To engage attendees -- even before your event,\u0026nbsp;\u003Ca href=\\\u0022https:\\\/\\\/blog.hubspot.com\\\/marketing\\\/how-to-promote-a-virtual-event\\\u0022 rel=\\\u0022noopener\\\u0022 target=\\\u0022_blank\\\u0022\u003Eyour promotional messages\u003C\\\/a\u003E, such as social posts or emails, can ask for people to submit their questions or comments beforehand.\u003C\\\/p\u003E\\n\\n\u003Cp\u003EAlso, if you have some type of webinar giveaway or special feature during the webinar, circulate that information to further differentiate your webinar from similar events held by competitors.\u003C\\\/p\u003E\\n\\n\u003Cp\u003EFor example, we once gave out tickets to \u003Ca href=\\\u0022https:\\\/\\\/www.inbound.com\\\/\\\u0022 rel=\\\u0022noopener\\\u0022 target=\\\u0022_blank\\\u0022\u003EINBOUND, our inbound marketing conference\u003C\\\/a\u003E, to a person who tweeted our webinar\u0027s hashtag before, during, and after the webinar. This helped us get audiences to participate in promotions on top of our other marketing efforts.\u0026nbsp;\u003C\\\/p\u003E\\n\\n\u003Cp\u003EFor more on promoting webinars and other virtual events,\u0026nbsp;\u003Ca href=\\\u0022https:\\\/\\\/blog.hubspot.com\\\/marketing\\\/how-to-promote-a-virtual-event\\\u0022 rel=\\\u0022noopener\\\u0022 target=\\\u0022_blank\\\u0022\u003Echeck out these tips from HubSpot experts\u003C\\\/a\u003E.\u003C\\\/p\u003E\\n\u0022},\u0022library\u0022:\u0022H5P.AdvancedText 1.1\u0022,\u0022subContentId\u0022:\u00220a4f200c-b2c6-498f-884b-ead03cc0b43d\u0022,\u0022metadata\u0022:{\u0022contentType\u0022:\u0022Text\u0022,\u0022license\u0022:\u0022U\u0022,\u0022title\u0022:\u0022Untitled Text\u0022}},\u0022title\u0022:\u00221. Interact with your audience through promotions before the webinar\u0022},{\u0022content\u0022:{\u0022params\u0022:{\u0022text\u0022:\u0022\u003Cp\u003ETo keep an audience engaged for 30 minutes to an hour, you\u0027ll need to give them something nice to look at. So,\u0026nbsp;\u003Ca href=\\\u0022https:\\\/\\\/blog.hubspot.com\\\/blog\\\/tabid\\\/6307\\\/bid\\\/34017\\\/How-to-Create-Top-Notch-Visual-Content-in-PowerPoint-Tutorial.aspx\\\u0022 rel=\\\u0022noopener\\\u0022 target=\\\u0022_blank\\\u0022\u003Emake your slide deck is visually appealing\u003C\\\/a\u003E.\u003C\\\/p\u003E\\n\\n\u003Cp\u003ECreate image-heavy slides that relate to the topic you are discussing. Using copy on slides is fine -- if done correctly. Don\u0027t simply write a paragraph on a slide in black and white. Instead, make sure the copy adds to the presentation. Stick to one color palette throughout the webinar deck, and try not to make it too busy.\u0026nbsp;\u003C\\\/p\u003E\\n\u0022},\u0022library\u0022:\u0022H5P.AdvancedText 1.1\u0022,\u0022subContentId\u0022:\u002200999928-5291-485b-8c8b-947d33c21baa\u0022,\u0022metadata\u0022:{\u0022contentType\u0022:\u0022Text\u0022,\u0022license\u0022:\u0022U\u0022,\u0022title\u0022:\u0022Untitled Text\u0022}},\u0022title\u0022:\u00222. Create an eye-popping slide deck\u0022},{\u0022content\u0022:{\u0022params\u0022:{\u0022text\u0022:\u0022\u003Cp\u003EAs mentioned in the first section, you can consider using a hashtag \u003Ca href=\\\u0022https:\\\/\\\/blog.hubspot.com\\\/blog\\\/tabid\\\/6307\\\/bid\\\/33651\\\/7-Tips-to-Kick-Your-Next-Marketing-Webinar-Up-a-Notch.aspx\\\u0022 rel=\\\u0022noopener\\\u0022 target=\\\u0022_blank\\\u0022\u003Ethrough the webinar marketing process\u003C\\\/a\u003E\u0026nbsp;that is unique to your virtual event. 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Dedicate a hashtag to your webinar\u0022},{\u0022content\u0022:{\u0022params\u0022:{\u0022text\u0022:\u0022\u003Cp\u003ENothing is worse on a webinar than a monotone speaker \u003Ca href=\\\u0022https:\\\/\\\/blog.hubspot.com\\\/blog\\\/tabid\\\/6307\\\/bid\\\/34149\\\/11-Steps-to-Make-Sure-Your-Next-Webinar-Is-a-Total-Flop.aspx\\\u0022 rel=\\\u0022noopener\\\u0022 target=\\\u0022_blank\\\u0022\u003Ewho puts the audience half asleep\u003C\\\/a\u003E. 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