Navigation

9-12 Algebra 2 Unit 6 Lesson 12

Gradeband

K-5 Math 6-8 Math •9-12 Math

Course

Algebra 1 Geometry •Algebra 2 Extra Support Materials for Algebra 1

Unit

Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 •Unit 6 Unit 7 Unit 8

Lesson

Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 Lesson 7 Lesson 8 Lesson 9 Lesson 10 Lesson 11 •Lesson 12 Lesson 13 Lesson 14 Lesson 15

K-5
6-8
9-12

Algebra 1
Geometry
Algebra 2
Extra Support Materials for Algebra 1

Integrated Math 1
Integrated Math 2
Integrated Math 3

Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6
Unit 7
Unit 8

Lesson 1
Lesson 2
Lesson 3
Lesson 4
Lesson 5
Lesson 6
Lesson 7
Lesson 8
Lesson 9
Lesson 10
Lesson 11
Lesson 12
Lesson 13
Lesson 14
Lesson 15

Lesson | Practice | Loading...

Sign in to access protected content and invite other educators

Sign in using your existing Kendall Hunt account. If you don’t have one, create an educator account.

Curriculum

IM K-5 Math
IM 6-8 Math
IM 9-12 Math

Professional Learning

Illustrative Mathematics® has operated as an independent 501(c)3 non-profit organization since 2013.

©2024 Illustrative Mathematics®. Licensed under CC BY-NC 4.0.

The Illustrative Mathematics name and logo are not subject to the Creative Commons license and may not be used without the prior and express written permission of Illustrative Mathematics.

This site includes public domain images or openly licensed images that are copyrighted by their respective owners. Openly licensed images remain under the terms of their respective licenses. See the image attribution section for more information.

Settings

Audience

Not all roles available for this page.

Assessment Access

Sign in to view assessments and invite other educators

Sign in using your existing Kendall Hunt account. If you don’t have one, create an educator account.

teacher
student
family

Unit 6, Lesson 12

Transformation Effects

Algebra 2

Practice

Problem 1

An original function is called \(f\). The function \(g\) is transformed from \(f\) using the following transformations, in this order:

Translate right 3
Stretch vertically by a factor of 4
Reflect over the \(x\)-axis

Write an equation for \(g(x)\) if \(f(x)\) is:

\(x^4\)
\(\frac1x \)
\(\sqrt[3]{x}\)

to access Practice Problem Solutions.

Problem 2

Describe the transformation from \(f(x)\) to \(g(x)\) if \(f(x)=x^3\) and \(g(x)\) is equal to:

\(\text-2(x+4)^3-1\)
\(\frac13\left(\frac13x\right)^3-3\)
\(5(\text-2x)^3\)

to access Practice Problem Solutions.

Problem 3

Describe the transformation from \(f(x)\) to \(g(x)\) if \(g(x)\) is equal to:

\(\text-4f(12x)-2\)
\(5f\left(\frac15x\right)+5\)
\(6f(x+3)-3\)

to access Practice Problem Solutions.

Problem 4

Match each function with the transformation that describes it.

The original function is \(y=\sqrt{x}\). The transformed function is \(y=\sqrt{\text-\frac12x}+6\).
The original function is \(y=\frac1x\). The transformed function is \(y=\text-\frac1{2(x+6)}\).
The original function is \(f(x)\). The transformed function is \(g(x)=\text-\frac12f(x+6)\).
The original function is \(f(x)\). The transformed function is \(g(x)=f\left(\text-\frac12x\right)+6\).

Reflect over \(x\)-axis

Shift left 6

Vertical stretch by a factor of \(\frac12\)
Reflect over \(y\)-axis

Shift up 6

Horizontal stretch by a factor of 2

to access Practice Problem Solutions.

Problem 5

ForLesson 11: Transforming from an Original Function

For each graph, an original function has undergone a transformation. Draw the graph of the transformed function if it has been reflected over the \(x\)-axis, stretched vertically by a factor of \(\frac12\), and shifted right 3.

$f(x)=2^x$

$g(x)=x^2$

$h(x)=\sqrt{x}$

to access Practice Problem Solutions.

Problem 6

ForLesson 11: Transforming from an Original Function

A graph has been transformed from an original function according to the following transformations. Select all of the transformations that affect the output of the function:

Vertical stretch by a factor of 2
Horizontal stretch by a factor of \(\frac 13\)
Shift left 5
Shift down 5
Reflect over the \(y\)-axis
Reflect over the \(x\)-axis

to access Practice Problem Solutions.

Lesson 12 Resources

Student Materials