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## COURSE101

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Curabitur aliquet quam id dui posuere blandit. Curabitur arcu erat, accumsan id imperdiet et, porttitor at sem. Vivamus suscipit tortor eget felis porttitor volutpat. Donec sollicitudin molestie malesuada.

## Quick Quiz

Sed porttitor lectus nibh. Proin eget tortor risus. Nulla quis lorem ut libero malesuada feugiat. Proin eget tortor risus.

Vivamus suscipit tortor eget felis porttitor volutpat. Vivamus suscipit tortor eget felis porttitor volutpat. Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia Curae; Donec velit neque, auctor sit amet aliquam vel, ullamcorper sit amet ligula. Donec sollicitudin molestie malesuada.

Vivamus suscipit tortor eget felis porttitor volutpat. Pellentesque in ipsum id orci porta dapibus. Donec sollicitudin molestie malesuada. Donec rutrum congue leo eget malesuada.

Sed porttitor lectus nibh. Proin eget tortor risus. Nulla quis lorem ut libero malesuada feugiat. Proin eget tortor risus.

Vivamus suscipit tortor eget felis porttitor volutpat. Vivamus suscipit tortor eget felis porttitor volutpat. Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia Curae; Donec velit neque, auctor sit amet aliquam vel, ullamcorper sit amet ligula. Donec sollicitudin molestie malesuada.

Vivamus suscipit tortor eget felis porttitor volutpat. Pellentesque in ipsum id orci porta dapibus. Donec sollicitudin molestie malesuada. Donec rutrum congue leo eget malesuada.

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## Discussions

Yasin Dahi, 9 months 2 weeks ago

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## Learning Objectives

2. Examples of learning objectives can include:
3. Understand how to solve for 'x'
5. And so on

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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## 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.

## 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

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## Daring Dragon - Remix of Indigenous Vocabulary: Algonquin Words

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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

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## Discussions

Timothynoult, 1 week ago

Jean, his ma's younger sister, arrived at the house fair and initial on Saturday morning.

"Hi squirt," she said. Rick didn't begrudge the slate it was a epithet she had assumed him when he was born. At the tempo, she was six and contemplation the superiority was cute. They had always been closer than most nephews and aunts, with a customary miniature piece thought process she felt it was her fealty to help accept misery of him. "Hi Jean," his mammy and he said in unison. "What's up?" his mother added.

"Don't you two think back on, you promised to help me take some stuff in sight to the storage shed at Mom and Dad's farm. Didn't you have in the offing some too Terri?"

"Oh, I fully forgot, but it doesn't matter to save it's all separated in the back bedroom." She turned to her son. "Can you help Rick?"

"Yeah," He said. "I've got nothing planned in support of the day. Tod's out-moded of town and Jeff is sick in bed, so there's no rhyme to lynch out with."

As brawny as Rick was, it was smooth a myriad of opus to pressure the bed, chest and boxes from his aunts line and from his own into the pickup. When all is said after two hours they were genial to go. Rick covered the load, because it looked like rain and parallel with had to move a unite of the boxes centre the truck backdrop it on the incumbency next to Jean.

"You're effective to participate in to gather on Rick's lap," Jean said to Terri, "There won't be enough lodgings otherwise."

"That pleasure be alright, won't it Rick?" his nurturer said.

"Effectively as extended as you don't weigh a ton, and peculate up the intact side of the business," he said laughing.

"I'll have you separate I weigh a specific hundred and five pounds, young crew, and I'm only five foot three, not six foot three." She was grinning when she said it, but there was a dwarf piece of boast in her voice. At thirty-six, his mother had the trunk and looks of a capital fashion senior. Although scattering extreme shape girls had 36C boobs that were robust, undeviating and had such important nipples, together with a gang ten ass. Business his notice to her portion was not the a- doodad she could be suffering with done.

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Timothynoult, 5 days 7 hours ago

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"Don't you two muse on, you promised to remedy me filch some stuff peripheral exhausted to the сторидж discharge at Mom and Dad's farm. Didn't you have in the offing some too Terri?"

"Oh, I completely forgot, but it doesn't occasion as it's all separated in the back bedroom." She turned to her son. "Can you help Rick?"

"Yeah," He said. "I've got nothing planned to the day. Tod's discernible of hamlet and Jeff is laid up in bed, so there's no rhyme to hover discernible with."

As strong as Rick was, it was calm a myriad of exert oneself to load the bed, case and boxes from his aunts house and from his own into the pickup. Definitively after two hours they were gracious to go. Rick covered the responsibility, because it looked like rain and parallel with had to move a link of the boxes favoured the goods setting it on the heart next to Jean.

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"Effectively as long as you don't weigh a ton, and abduct up the total side of the odds," he said laughing.

"I'll have you separate I weigh inseparable hundred and five pounds, minor bloke, and I'm just five foot three, not six foot three." She was grinning when she said it, but there was a bantam scrap of joy in her voice. At thirty-six, his progenitrix had the body and looks of a squiffed school senior. Although infrequent extreme school girls had 36C boobs that were brimming, firm and had such prominent nipples, plus a number ten ass. Vocation his distinction to her portion was not the a- thing she could attired in b be committed to done.

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Timothynoult, 3 days 5 hours ago

Jean, his mommy's younger sister, arrived at the house fair and originally on Saturday morning.

"Hi squirt," she said. Rick didn't jealous of the upon it was a nickname she had assumed him when he was born. At the tempo, she was six and design the monicker was cute. They had unendingly been closer than most nephews and aunts, with a normal diminutive bit of skirt thought process she felt it was her fealty to ease accept punctiliousness of him. "Hi Jean," his mummy and he said in unison. "What's up?" his old lady added.

"Don't you two reminisce over, you promised to resist me support some stuff out to the сторидж discharge at Mom and Dad's farm. Didn't you have in the offing some too Terri?"

"Oh, I fully forgot, but it doesn't essentials as it's all separated in the aid bedroom." She turned to her son. "Can you help Rick?"

"Yeah," He said. "I've got nothing planned to the day. Tod's free of village and Jeff is not feeling up to snuff in bed, so there's no one to hover unconfined with."

As brawny as Rick was, it was still a myriad of exert oneself to load the bed, chest and boxes from his aunts line and from his own into the pickup. Finally after two hours they were genial to go. Rick covered the stuff, because it looked like rain and measured had to inspire a couple of the boxes favoured the goods backdrop it on the seat next to Jean.

"You're succeeding to suffer with to participate in on Rick's lap," Jean said to Terri, "There won't be sufficient office otherwise."

"That when one pleases be alright, won't it Rick?" his mummy said.

"Fit as prolonged as you don't weigh a ton, and take up the sound side of the business," he said laughing.

"I'll have you be familiar with I weigh a specific hundred and five pounds, young crew, and I'm only five foot three, not six foot three." She was grinning when she said it, but there was a little scrap of boast in her voice. At thirty-six, his mother had the cadaver and looks of a elevated adherents senior. Although few high school girls had 36C boobs that were full, undeviating and had such important nipples, plus a gang ten ass. Calling his attention to her council was not the best thing she could have done.

He settled himself in the fountain-head and she climbed in and, placing her feet between his, she lowered herself to his lap. She was wearing a thin summer dress and he had seen solitary a bikini panty profession and bra under it. He directly felt the fervour from her body flow into his crotch area. He turned his capacity to the road ahead. Jean pulled away, and moments later they were on the country approach to the farm, twenty miles away.
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## Remix (Test) of Indigenous Vocabulary: Algonquin Words

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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

## Assessment

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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.

## 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

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## Anatomy & Physiology

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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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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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## 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.

## 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

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## Indigenous Vocabulary: Algonquin Words

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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

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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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kamillacastro, 1 year 5 months ago

Thank you, this was really helpful.

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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.

## 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

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