Subjects

Algebra 2

Complex numbers & unit i

The imaginary unit i

Easy Steps for Graphing Absolute Value Transformations: Worksheets and Fun Calculators

Name: Knowunity
Brand: Knowunity

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Easy Steps for Graphing Absolute Value Transformations: Worksheets and Fun Calculators

Asna Kadiwal

@onlyy_asna

2 Followers

Absolute Value Functions and Transformations: A Comprehensive Guide

This guide covers the fundamentals of absolute value functions, their transformations, and solving absolute value equations and inequalities. It provides step-by-step instructions, examples, and practice problems to help students master these concepts.

• Explains the definition and properties of absolute value functions
• Covers transformations of absolute value functions and graphing techniques
• Demonstrates methods for solving absolute value equations and inequalities
• Includes practice problems and challenge questions for reinforcement

10/5/2023

261

Absolute value notes Day 1
1. Absolute value of a number is the distance from 0 on a
number line. It represents positive distance without di

Advanced Absolute Value Equations

This page provides more complex examples of solving absolute value equations and introduces challenge problems.

Example: Solve |4 - 3x| = 2x + 3 • Positive case: 4 - 3x = 2x + 3 • Negative case: -(4 - 3x) = 2x + 3 • Solutions: x = 1/5 and x = 7

Highlight: When solving equations with absolute value expressions on both sides, it's crucial to consider all possible combinations of positive and negative cases.

Challenge Question: Solve |7x - 3| = |3x + 7| • Solution: x = -2/5 or x = 5/2

View

Solving Absolute Value Equations

This page introduces techniques for solving absolute value equations, including graphical and algebraic methods.

Highlight: To solve an absolute value equation:

Isolate the absolute value
Set up two cases: positive and negative
Solve each case
Check for extraneous solutions

Example: Solve |2x + 4| = 6x + 28 • Positive case: 2x + 4 = 6x + 28 • Negative case: -(2x + 4) = 6x + 28 • Solution: x = -4 (after checking for extraneous solutions)

Vocabulary: An extraneous solution is a solution that satisfies the equation algebraically but not in the context of absolute value.

View

Practice Problems and Solutions

This final page provides additional practice problems and their solutions to reinforce the concepts learned throughout the guide.

Example: Solve |-4y + 2| = 10 • Positive case: -4y + 2 = 10 • Negative case: -(-4y + 2) = 10 • Solutions: y = -2 or y = 3

Highlight: When solving absolute value inequalities, remember to: • Flip the inequality sign when multiplying or dividing by a negative number • Consider that an absolute value cannot be less than a negative number • Recognize that an absolute value is always greater than a negative number

This comprehensive guide equips students with the knowledge and skills needed to tackle absolute value transformations, equations, and inequalities with confidence.

View

Absolute Value Inequalities

This page introduces the concept of absolute value inequalities and methods for solving them.

Definition: An absolute value inequality is an inequality that involves an absolute value expression.

Types of absolute value inequalities:

|ax + b| < c (AND type)
|ax + b| > c (OR type)

Highlight: To solve an absolute value inequality:

Isolate the absolute value
Set up two cases: positive and negative
Solve each case
Combine the solutions appropriately

Example: Solve |4x - 8| > 12 • Positive case: 4x - 8 > 12 • Negative case: -(4x - 8) > 12 • Solution: x < -1 or x > 5

View

Absolute Value Functions: Fundamentals and Properties

This page introduces the concept of absolute value and explores the properties of the absolute value parent function.

Definition: The absolute value of a number is its distance from 0 on a number line, representing positive distance without direction.

The absolute value function is defined by a piecewise function:

f(x) = |x| = { x if x ≥ 0 -x if x < 0

Highlight: The absolute value parent function graph has several key properties:

• Domain: All real numbers (-∞, ∞) • Range: [0, ∞) • Vertex: (0,0) • Axis of Symmetry: x = 0 • Interval of Increase: (0, ∞) • Interval of Decrease: (-∞, 0)

Example: The graph of the absolute value parent function resembles a "V" shape, with its vertex at the origin and equal slopes on both sides.

View

Absolute Value Transformations and Graphing Techniques

This page covers the transformation of absolute value functions and introduces methods for graphing these transformed functions.

The general form of an absolute value transformation function is:

g(x) = A|B(x - C)| + D

Where: • A affects the vertical stretch or compression and reflection • B affects the horizontal stretch or compression • C affects the horizontal shift • D affects the vertical shift

Highlight: The vertex of the transformed function is always at the point (C, D).

Two methods for graphing absolute value transformations are presented:

Transformation Method: Apply transformation rules to the parent function points.
Point-by-Point Method: Use the function to calculate new points.

Example: For the function g(x) = -2|½(x + 2)| + 1: • Vertex: (-2, 1) • Points: (-2.5, -3), (-1.5, -3), (-2, 1)

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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.

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

Subjects

Algebra 2

Complex numbers & unit i

The imaginary unit i

Easy Steps for Graphing Absolute Value Transformations: Worksheets and Fun Calculators

Asna Kadiwal

@onlyy_asna

2 Followers

Absolute Value Functions and Transformations: A Comprehensive Guide

10/5/2023

261

9th/10th

Algebra 2

Advanced Absolute Value Equations

This page provides more complex examples of solving absolute value equations and introduces challenge problems.

Example: Solve |4 - 3x| = 2x + 3 • Positive case: 4 - 3x = 2x + 3 • Negative case: -(4 - 3x) = 2x + 3 • Solutions: x = 1/5 and x = 7

Highlight: When solving equations with absolute value expressions on both sides, it's crucial to consider all possible combinations of positive and negative cases.

Challenge Question: Solve |7x - 3| = |3x + 7| • Solution: x = -2/5 or x = 5/2

Solving Absolute Value Equations

This page introduces techniques for solving absolute value equations, including graphical and algebraic methods.

Highlight: To solve an absolute value equation:

Isolate the absolute value
Set up two cases: positive and negative
Solve each case
Check for extraneous solutions

Example: Solve |2x + 4| = 6x + 28 • Positive case: 2x + 4 = 6x + 28 • Negative case: -(2x + 4) = 6x + 28 • Solution: x = -4 (after checking for extraneous solutions)

Vocabulary: An extraneous solution is a solution that satisfies the equation algebraically but not in the context of absolute value.

Practice Problems and Solutions

This final page provides additional practice problems and their solutions to reinforce the concepts learned throughout the guide.

Example: Solve |-4y + 2| = 10 • Positive case: -4y + 2 = 10 • Negative case: -(-4y + 2) = 10 • Solutions: y = -2 or y = 3

Highlight: When solving absolute value inequalities, remember to: • Flip the inequality sign when multiplying or dividing by a negative number • Consider that an absolute value cannot be less than a negative number • Recognize that an absolute value is always greater than a negative number

This comprehensive guide equips students with the knowledge and skills needed to tackle absolute value transformations, equations, and inequalities with confidence.

Absolute Value Inequalities

This page introduces the concept of absolute value inequalities and methods for solving them.

Definition: An absolute value inequality is an inequality that involves an absolute value expression.

Types of absolute value inequalities:

|ax + b| < c (AND type)
|ax + b| > c (OR type)

Highlight: To solve an absolute value inequality:

Isolate the absolute value
Set up two cases: positive and negative
Solve each case
Combine the solutions appropriately

Example: Solve |4x - 8| > 12 • Positive case: 4x - 8 > 12 • Negative case: -(4x - 8) > 12 • Solution: x < -1 or x > 5

Absolute Value Functions: Fundamentals and Properties

This page introduces the concept of absolute value and explores the properties of the absolute value parent function.

Definition: The absolute value of a number is its distance from 0 on a number line, representing positive distance without direction.

The absolute value function is defined by a piecewise function:

f(x) = |x| = { x if x ≥ 0 -x if x < 0

Highlight: The absolute value parent function graph has several key properties:

• Domain: All real numbers (-∞, ∞) • Range: [0, ∞) • Vertex: (0,0) • Axis of Symmetry: x = 0 • Interval of Increase: (0, ∞) • Interval of Decrease: (-∞, 0)

Example: The graph of the absolute value parent function resembles a "V" shape, with its vertex at the origin and equal slopes on both sides.

Absolute Value Transformations and Graphing Techniques

This page covers the transformation of absolute value functions and introduces methods for graphing these transformed functions.

The general form of an absolute value transformation function is:

g(x) = A|B(x - C)| + D

Where: • A affects the vertical stretch or compression and reflection • B affects the horizontal stretch or compression • C affects the horizontal shift • D affects the vertical shift

Highlight: The vertex of the transformed function is always at the point (C, D).

Two methods for graphing absolute value transformations are presented:

Transformation Method: Apply transformation rules to the parent function points.
Point-by-Point Method: Use the function to calculate new points.

Example: For the function g(x) = -2|½(x + 2)| + 1: • Vertex: (-2, 1) • Points: (-2.5, -3), (-1.5, -3), (-2, 1)

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.

Download in

Google Play

Download in

App Store

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

Easy Steps for Graphing Absolute Value Transformations: Worksheets and Fun Calculators

Advanced Absolute Value Equations

Solving Absolute Value Equations

Practice Problems and Solutions

Absolute Value Inequalities

Absolute Value Functions: Fundamentals and Properties

Absolute Value Transformations and Graphing Techniques

Similar Content

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.

4.9+

13 M

#1

950 K+

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

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

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

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

Easy Steps for Graphing Absolute Value Transformations: Worksheets and Fun Calculators

Advanced Absolute Value Equations

Solving Absolute Value Equations

Practice Problems and Solutions

Absolute Value Inequalities

Absolute Value Functions: Fundamentals and Properties

Absolute Value Transformations and Graphing Techniques

Similar Content

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.

4.9+

13 M

#1

950 K+

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

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

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

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