# To sketch the graph of the function.

### 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 63E

a.

To determine

## To sketch the graph of the function.

Expert Solution

### Explanation of Solution

Given information:

The function is y=f(x)

Graph :

the graph obtained as:

Interpretation: from the above graph it is observed that when y=f(x) is given, the graph of the function y=f(x2) is obtained by shifting the graph of y=f(x) to the right 2 units.

b.

To determine

Expert Solution

### Explanation of Solution

Given information:

The function is y=f(x)

Graph :

The graph obtained as:

Interpretation: from the above graph it is observed that when y=f(x) is given, the graph of the function y=f(x)2 is obtained by shifting the graph of y=f(x) to the downwards 2 units.

c.

To determine

Expert Solution

### Explanation of Solution

Given information:

The function is y=f(x)

Graph :

The graph obtained as:

Interpretation: from the above graph it is observed that when y=f(x) is given, the graph of the function y=2f(x) is obtained by vertically stretching the graph of y=f(x) by the factor of 2 .

d.

To determine

Expert Solution

### Explanation of Solution

Given information:

The function is y=f(x)

Graph :

The graph obtained as:

Interpretation: from the above graph it is observed that when y=f(x) is given, the graph of the function y=f(x)+3 is obtained by reflecting the graph of y=f(x) in the x -axis then shift upwards by 3 units.

f.

To determine

Expert Solution

### Explanation of Solution

Given information:

The function is y=f(x)

Graph :

The graph obtained as:

Interpretation: from the above graph it is observed that when y=f(x) is given, the graph of the function y=f(x) is obtained by reflecting the graph of y=f(x) in the y -axis .

e.

To determine

Expert Solution

### Explanation of Solution

Given information:

The function is y=f(x)

Graph :

The graph obtained as:

Interpretation: from the above graph it is observed that when y=f(x) is given, the graph of the function y=12f(x1) is obtained by vertically shrinking the graph of y=f(x) by the factor of 12 then shift right by 1 unit .

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