# To describe how the graph of the function can be obtained from the graph of y = 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 19E

a.

To determine

## To describe how the graph of the function can be obtained from the graph of y=x2 .

Expert Solution

The graph of g(x)=x2+1 is obtained by shifting the graph of f(x)=x2 to the upward 1 units.

### Explanation of Solution

Given information :

The functionsis g(x)=x2+1 .

Use the definition of vertical shifts of graphs,

When graph of f(x)=x2 is given, then for function g(x)=x2+1 ,shift the graph of f(x)=x2 upward 1 units.

b.

To determine

### To describe how the graph of the function can be obtained from the graph of y=x2 .

Expert Solution

The graph of g(x)=(x1)2 is obtained by shifting the graph of f(x)=x2 to the right 1 units.

### Explanation of Solution

Given information :

The functionsis g(x)=(x1)2 .

Use the definition of horizontal shifts of graphs,

When graph of f(x)=x2 is given, then for function g(x)=(x1)2 ,shift the graph of f(x)=x2 right 1 units.

c.

To determine

### To describe how the graph of the function can be obtained from the graph of y=x2 .

Expert Solution

The graph of g(x)=x2 is obtained by reflecting the graph of f(x)=x2 in the x- axis.

### Explanation of Solution

Given information :

The functionsis g(x)=x2 .

Use the definition of reflecting of graphs,

When graph of f(x)=x2 is given, then for function g(x)=x2 , reflect the graph of f(x)=x2 in the x- axis.

d.

To determine

### To describe how the graph of the function can be obtained from the graph of y=x2 .

Expert Solution

The graph of g(x)=(x1)2+3 is obtained by shifting the graph of f(x)=x2 to the right 1 units then shift upward by 3 unit.

### Explanation of Solution

Given information :

The functionsis g(x)=(x1)2+3 .

Use the definition of vertical and horizontal shifts of graphs,

When graph of f(x)=x2 is given, then for function g(x)=(x1)2+3 ,shift the graph of f(x)=x2 right 1 units then shift upward by 3 unit.

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