# The process to find the function y = − f ( x ) from the function f ( x ) . ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805 ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter T, Problem 4CDT

(a)

To determine

## To find: The process to find the function y=−f(x) from the function f(x).

Expert Solution

### Explanation of Solution

According to the reflection of the function, the graph of the function y=f(x) is obtained if the graph of y=f(x) is reflected vertically about x-axis.

Thus, the function y=f(x) has to be reflected in order to obtain the function y=f(x).

(b)

To determine

Expert Solution

### Explanation of Solution

According to the magnification of the function the graph of the function y=kf(x) is obtained if the graph of y=f(x) is shrunken by k times.

Thus, the function y=2f(x) is obtained if the graph of y=f(x) is shrunken by k times.

According to the translation and reflection of the function the graph of the function y=f(x)+k is obtained if the graph of y=f(x) is translated upward by k units.

The graph of the function y=2f(x)1 is obtained if the graph of y=2f(x) is translated downward by 1 units.

(c)

To determine

Expert Solution

### Explanation of Solution

The graph of the function y=f(xh) is obtained if the graph of y=f(x) is translated right by h units.

Thus, the graph of the function y=f(x3) is obtained if the graph of y=f(x) is translated right by 3 units.

The graph of the function y=f(x)+k is obtained if the graph of y=f(x) is translated upward by k units.

Thus, the graph of the function y=f(x3)+2 is obtained if the graph of y=f(x3) is translated upward by 2 units.

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