# To describe how the graph of the function can be obtained from the graph of f ( x ) = 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 20E

a.

To determine

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

Expert Solution

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

### Explanation of Solution

Given information :

The function is g(x)=x2 .

Use the definition of horizontal shifts of graphs,

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

b.

To determine

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

Expert Solution

The graph of g(x)=x+1 is obtained by shifting the graph of f(x)=x to the upward 1 units.

### Explanation of Solution

Given information :

The function is g(x)=x+1 .

Use the definition of vertical shifts of graphs,

When graph of f(x)=x is given, then for function g(x)=x+1 ,shift the graph of f(x)=x upward 1 unit.

c.

To determine

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

Expert Solution

The graph of g(x)=x+2+2 is obtained by shifting the graph of f(x)=x to the left 2 unit and then shift upward 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 unit and then shift upward by 2 units.

d.

To determine

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

Expert Solution

The graph of g(x)=x+1 is obtained by reflecting the graph of f(x)=x in the x -axis then shift upward by 1 units.

### Explanation of Solution

Given information :

The function is g(x)=x+1 .

Use the definition of and reflecting and verticalshifts of graphs,

When graph of f(x)=x is given, then for function g(x)=x+1 ,reflect the graph of f(x)=x in the x -axis then shift upward by 1 units.

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