# 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 1.3, Problem 2E

(a)

To determine

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

Expert Solution

The 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) .

Since 8 is added to f(x) , the graph of y=f(x)+8 is shifted 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

The 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) .

Since 8 is added to x , the graph y=f(x+8) is shifted 8 units to the left.

(c)

To determine

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

Expert Solution

The graph stretched 8 units vertically.

### Explanation of Solution

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

Since 8 is multiplied to f(x) , the graph y=8f(x) is stretched 8 units vertically.

(d)

To determine

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

Expert Solution

The graph shrunk 8 units horizontally.

### Explanation of Solution

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

Since 8 is multiplied to x, the graph y=f(8x) is shrunk 8 units horizontally.

(e)

To determine

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

Expert Solution

The graph reflects the x-axis and shifted 1 unit downward.

### Explanation of Solution

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

Since it is f(x) the graph is an odd function, it reflects about the x-axis.

Also, the graph y=f(x)1 is shifted 1 unit downward.

(f)

To determine

Expert Solution