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Graphs of absolute value functions

Algebra 2 Functions: Parent Functions and Linear Equations Worksheet with Answers (PDF)

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Algebra 2 Functions: Parent Functions and Linear Equations Worksheet with Answers (PDF)
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ChoCho

@choyi_tsyz

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A comprehensive guide to parent functions, transformations, and mathematical notations, focusing on various function types and their graphical representations. The material covers essential concepts in algebra including parent functions and transformations examples and different methods of analyzing functions.

• The guide extensively covers types of functions Algebra 2, including linear, absolute value, quadratic, square root, and cube root functions
• Detailed explanations of function transformations including vertical/horizontal shifts, reflections, and stretches
• In-depth coverage of domain and range concepts using set notation
• Practical examples demonstrating linear function examples with answers and various transformation techniques
• Comprehensive analysis of parent functions and transformations with visual representations

5/11/2023

1205

<h2 id="linearfunctions">Linear Functions</h2> <p>Linear functions are written in the form y = mx + b, where the constant slope (m-value) c

View

Page 4: Reflections and Transformations

The fourth page covers reflections across both x and y axes, explaining how these transformations affect function graphs.

Definition: Reflection in the x-axis is determined by the sign of the a-value in the function.

Highlight: In y-axis reflection, only the x-value is affected, creating a mirror image across the y-axis.

<h2 id="linearfunctions">Linear Functions</h2> <p>Linear functions are written in the form y = mx + b, where the constant slope (m-value) c

View

Page 3: Function Transformations

This page explains how equations reflect various transformations of functions, focusing on vertical and horizontal translations.

Definition: Vertical translation occurs when a k-value is added or subtracted from the function.

Example: In the equation y = a(x-h)² + k, the k-value determines vertical shift while h-value determines horizontal shift.

Highlight: Positive k-values shift the graph up, while negative k-values shift the graph down.

<h2 id="linearfunctions">Linear Functions</h2> <p>Linear functions are written in the form y = mx + b, where the constant slope (m-value) c

View

Page 1: Introduction to Basic Function Types

This page introduces fundamental function types including linear, absolute value, and quadratic functions. Each function type is explained with its unique characteristics and graphical representations.

Definition: A linear function is written in the form y = mx + b, where m represents the slope and b represents the y-intercept.

Example: The parent function for linear functions is y = x, which creates a straight line when graphed.

Highlight: Absolute value functions create V-shaped graphs with mirror image properties on either side.

Vocabulary: A parabola is the U-shaped graph formed by quadratic functions.

<h2 id="linearfunctions">Linear Functions</h2> <p>Linear functions are written in the form y = mx + b, where the constant slope (m-value) c

View

Page 2: Advanced Function Types

The second page delves into square root and cube root functions, expanding on the basic function types introduced earlier.

Definition: Square root functions have the form y = √x and create a flattened curve starting at the origin.

Highlight: Square root functions can be viewed as sideways parabolas existing only in the first quadrant.

Example: Cube root functions create an elongated S-shape and have the form y = ³√x.

<h2 id="linearfunctions">Linear Functions</h2> <p>Linear functions are written in the form y = mx + b, where the constant slope (m-value) c

View

Pages 6-7: Domain and Range

The final pages focus on domain and range concepts using set notation and practical examples.

Definition: Domain represents all possible x-values, while range represents all possible y-values.

Example: For a square root function with vertex at (4,0), the domain is {x|x ∈ R, x ≥ -4}.

Highlight: Domain and range can be determined by analyzing the graph's behavior and limitations.

<h2 id="linearfunctions">Linear Functions</h2> <p>Linear functions are written in the form y = mx + b, where the constant slope (m-value) c

View

Page 5: Function Stretches and Shrinks

This section details vertical and horizontal stretches and shrinks of functions.

Definition: Vertical stretches and shrinks are controlled by the a-value multiplier.

Example: When |a| > 1, the graph stretches; when 0 < |a| < 1, the graph shrinks.

Highlight: Horizontal transformations affect only the x-value and use the reciprocal of the given factor.

<h2 id="linearfunctions">Linear Functions</h2> <p>Linear functions are written in the form y = mx + b, where the constant slope (m-value) c

View

<h2 id="linearfunctions">Linear Functions</h2> <p>Linear functions are written in the form y = mx + b, where the constant slope (m-value) c

View

<h2 id="linearfunctions">Linear Functions</h2> <p>Linear functions are written in the form y = mx + b, where the constant slope (m-value) c

View

<h2 id="linearfunctions">Linear Functions</h2> <p>Linear functions are written in the form y = mx + b, where the constant slope (m-value) c

View

Similar Content

Know Parent Functions thumbnail

4

87

9th/10th

Parent Functions

About the Know: starred functions are the most common one when beginning Algebra. There’s also some minor information about Domain and Range.

Can't find what you're looking for? Explore other subjects.

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Subjects

/

Algebra 1

/

Functions

/

Graphs of absolute value functions

Algebra 2 Functions: Parent Functions and Linear Equations Worksheet with Answers (PDF)

user profile picture

ChoCho

@choyi_tsyz

·

30 Followers

Follow

A comprehensive guide to parent functions, transformations, and mathematical notations, focusing on various function types and their graphical representations. The material covers essential concepts in algebra including parent functions and transformations examples and different methods of analyzing functions.

• The guide extensively covers types of functions Algebra 2, including linear, absolute value, quadratic, square root, and cube root functions
• Detailed explanations of function transformations including vertical/horizontal shifts, reflections, and stretches
• In-depth coverage of domain and range concepts using set notation
• Practical examples demonstrating linear function examples with answers and various transformation techniques
• Comprehensive analysis of parent functions and transformations with visual representations

5/11/2023

1205

 

9th

 

Algebra 1

471

<h2 id="linearfunctions">Linear Functions</h2> <p>Linear functions are written in the form y = mx + b, where the constant slope (m-value) c

Page 4: Reflections and Transformations

The fourth page covers reflections across both x and y axes, explaining how these transformations affect function graphs.

Definition: Reflection in the x-axis is determined by the sign of the a-value in the function.

Highlight: In y-axis reflection, only the x-value is affected, creating a mirror image across the y-axis.

<h2 id="linearfunctions">Linear Functions</h2> <p>Linear functions are written in the form y = mx + b, where the constant slope (m-value) c

Page 3: Function Transformations

This page explains how equations reflect various transformations of functions, focusing on vertical and horizontal translations.

Definition: Vertical translation occurs when a k-value is added or subtracted from the function.

Example: In the equation y = a(x-h)² + k, the k-value determines vertical shift while h-value determines horizontal shift.

Highlight: Positive k-values shift the graph up, while negative k-values shift the graph down.

<h2 id="linearfunctions">Linear Functions</h2> <p>Linear functions are written in the form y = mx + b, where the constant slope (m-value) c

Page 1: Introduction to Basic Function Types

This page introduces fundamental function types including linear, absolute value, and quadratic functions. Each function type is explained with its unique characteristics and graphical representations.

Definition: A linear function is written in the form y = mx + b, where m represents the slope and b represents the y-intercept.

Example: The parent function for linear functions is y = x, which creates a straight line when graphed.

Highlight: Absolute value functions create V-shaped graphs with mirror image properties on either side.

Vocabulary: A parabola is the U-shaped graph formed by quadratic functions.

<h2 id="linearfunctions">Linear Functions</h2> <p>Linear functions are written in the form y = mx + b, where the constant slope (m-value) c

Page 2: Advanced Function Types

The second page delves into square root and cube root functions, expanding on the basic function types introduced earlier.

Definition: Square root functions have the form y = √x and create a flattened curve starting at the origin.

Highlight: Square root functions can be viewed as sideways parabolas existing only in the first quadrant.

Example: Cube root functions create an elongated S-shape and have the form y = ³√x.

<h2 id="linearfunctions">Linear Functions</h2> <p>Linear functions are written in the form y = mx + b, where the constant slope (m-value) c

Pages 6-7: Domain and Range

The final pages focus on domain and range concepts using set notation and practical examples.

Definition: Domain represents all possible x-values, while range represents all possible y-values.

Example: For a square root function with vertex at (4,0), the domain is {x|x ∈ R, x ≥ -4}.

Highlight: Domain and range can be determined by analyzing the graph's behavior and limitations.

<h2 id="linearfunctions">Linear Functions</h2> <p>Linear functions are written in the form y = mx + b, where the constant slope (m-value) c

Page 5: Function Stretches and Shrinks

This section details vertical and horizontal stretches and shrinks of functions.

Definition: Vertical stretches and shrinks are controlled by the a-value multiplier.

Example: When |a| > 1, the graph stretches; when 0 < |a| < 1, the graph shrinks.

Highlight: Horizontal transformations affect only the x-value and use the reciprocal of the given factor.

<h2 id="linearfunctions">Linear Functions</h2> <p>Linear functions are written in the form y = mx + b, where the constant slope (m-value) c
<h2 id="linearfunctions">Linear Functions</h2> <p>Linear functions are written in the form y = mx + b, where the constant slope (m-value) c
<h2 id="linearfunctions">Linear Functions</h2> <p>Linear functions are written in the form y = mx + b, where the constant slope (m-value) c
<h2 id="linearfunctions">Linear Functions</h2> <p>Linear functions are written in the form y = mx + b, where the constant slope (m-value) c

Similar Content

Algebra 1 - Parent Functions

About the Know: starred functions are the most common one when beginning Algebra. There’s also some minor information about Domain and Range.

4

87

0

Know Parent Functions thumbnail

Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

Ranked #1 Education App

Download in

Google Play

Download in

App Store

Knowunity is the # 1 ranked education app in five European countries

4.9+

Average App Rating

13 M

Students use Knowunity

#1

In Education App Charts in 12 Countries

950 K+

Students uploaded study notes

Still not sure? Look at what your fellow peers are saying...

iOS User

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

Stefan S, iOS User

The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User

Love this App ❤️, I use it basically all the time whenever I'm studying