# To describe how the graph of the function can be obtained from the graph of f ( x ) = x 2 . ### 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 15E

a.

To determine

## To describe how the graph of the function can be obtained from the graph of f(x)=x2 .

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.

### Explanation of Solution

Given information :

The function is g(x)=(x+2)2  .

use definition of horizontal shifts of graph,

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

b.

To determine

### To describe how the graph of the function can be obtained from the graph of f(x)=x2 .

Expert Solution

The graph of g(x)=x2+2 is obtained by shifting the graph of f(x)=x2 to the upwards 2 units.

### Explanation of Solution

Given information :

The function is g(x)=x2+2  .

use definition of vertical shifts of graph,

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

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