7 Section 1.8 Transformations of Functions

1. The parent function graph is given below, [latex]f(x)[/latex]. For each child function, describe in words the transformations that are being performed, then draw a graph of the child function.

Piecewise parent function for transformation

a. [latex]g(x)=f(x-2)+1[/latex]

b. [latex]h(x)=\frac{1}{2}f(x)-2[/latex]

 

Show Solution

Answers

a. To make [latex]g(x)[/latex], [latex]f(x)[/latex] has been shifted right 2 units, and up 1.

Child function of a transformed parent function

b. To make [latex]h(x)[/latex], [latex]f(x)[/latex] has been vertically compressed by [latex]\frac{1}{2}[/latex] and shifted down 2.

Transformed function of parent f(x)

 

2.  Given the parent function [latex]g(x)=\sqrt{x}[/latex], write the equations of each child function described below.

a. Child function [latex]h(x)[/latex] is [latex]g(x)[/latex] that has been shifted left 3 units, reflected across the [latex]x[/latex]-axis and shifted up 4 units.

b. Child function [latex]k(x)[/latex] is [latex]g(x)[/latex] that has been reflected across the [latex]y[/latex]-axis, and vertically stretched by 5.

 

Show Solution

Answers

a. [latex]h(x)=-\sqrt{x+3}+4[/latex]

b. [latex]k(x)=5\sqrt{-x}[/latex]

 

License

Additional Examples Copyright © by Marcela Gutierrez and Sherri Spriggs. All Rights Reserved.

Share This Book