# To describe how the graph of the function can be obtained from the graph of y = | x | . ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071 ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 2.5, Problem 17E

a.

To determine

## To describe how the graph of the function can be obtained from the graph of y=|x| .

Expert Solution

The graph of g(x)=|x+2|2 is obtained by shifting the graph of f(x)=x2 to the left 2 units then shift downward by 2 units.

### Explanation of Solution

Given information :

The function is g(x)=|x+2|2  .

Use the definition of vertical and horizontal shifts of graphs,

When graph of f(x)=|x| is given, then for function g(x)=|x+2|2 , shift the graph of f(x)=|x| to the left 2 units then shift downward by 2 units.

b.

To determine

### To describe how the graph of the function can be obtained from the graph of y=|x| .

Expert Solution

The graph of g(x)=|x2|+2 is obtained by shifting the graph of f(x)=x2 to the right 2 units then shift upward by 2 units.

### Explanation of Solution

Given information :

The function is g(x)=|x2|+2 .

Use the definition of vertical and horizontal shifts of graphs,

When graph of f(x)=|x| is given, then for function g(x)=|x2|+2 , shift the graph of f(x)=|x| to the right 2 units then shift upward by 2 units.

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