# How the graph y = f ( x ) + 8 is obtained from the graph of y = 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 1, Problem 9RE

(a)

To determine

## To explain: How the graph y=f(x)+8 is obtained from the graph of y=f(x).

Expert Solution

Solution:

The y=f(x) graph shifted 8 units upward.

### Explanation of Solution

It is given that the graph y=f(x)+8 is obtained from the graph of y=f(x).

The graph of y=f(x)+8 can be obtained by shifting the graph y=f(x) by 8 units upward.

(b)

To determine

### To explain: How the graph y=f(x+8) is obtained from the graph of y=f(x).

Expert Solution

Solution:

The y=f(x) graph shifted 8 units to the left.

### Explanation of Solution

It is given that the graph y=f(x+8) is obtained from the graph of y=f(x).

The graph of y=f(x+8) can be obtained by shifting the graph y=f(x) by 8 units to the left.

(c)

To determine

### To explain: How the graph y=1+2f(x) is obtained from the graph of y=f(x).

Expert Solution

Solution:

The y=f(x) graph stretched 2 units vertically and then shifted 1 unit upward.

### Explanation of Solution

It is given that the graph y=1+2f(x) is obtained from the graph of y=f(x).

The graph of y=1+2f(x) can be obtained by stretching the graph y=f(x) vertically by a factor of 2 and then shifting 1 unit upward.

(d)

To determine

### To explain: How the graph y=f(x−2)−2 is obtained from the graph of y=f(x).

Expert Solution

Solution:

The y=f(x) graph shifted 2 units to the right and then shifted 2 units downward.

### Explanation of Solution

It is given that the graph y=f(8x) is obtained from the graph of y=f(x).

The graph of y=f(x2)2 can be obtained by shifting the graph y=f(x) by 2 units to the right and then 2 units downward.

(e)

To determine

### To write: How the graph y=−f(x) is obtained from the graph of y=f(x).

Expert Solution

Solution:

The y=f(x) graph reflected about the x-axis.

### Explanation of Solution

It is given that the graph y=f(x) can be obtained from the graph of y=f(x). The graph of y=f(x) can be obtained by reflecting the graph y=f(x) about the x-axis.

(f)

To determine

### To write: How the graph y=f−1(x) is obtained from the graph of y=f(x).

Expert Solution

Solution:

The y=f(x) graph is reflected about the line y = x.

### Explanation of Solution

It is given that the graph y=f1(x) is obtained from the graph of y=f(x).

The graph of y=f1(x) can be obtained by reflecting the graph y=f(x) about the line y=x.

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