# The way to obtain the graph of y = f ( x ) + 8 with the help of graph of f ( x ) .

### 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, Problem 63RE

(a)

To determine

## To find: The way to obtain the graph of y=f(x)+8 with the help of graph of f(x) .

Expert Solution

To obtain the graph of y=f(x)+8 from the graph of f(x) shift the graph of f(x) upwards by 8 units.

### Explanation of Solution

Given information:

The graph of f(x) is given.

Calculation:

The graph of function f(x) is given and the function y=f(x)+8 increases the value of f(x) by 8 units.

Shift the graph of f(x) upwards by 8 units for the graph of y=f(x)+8 .

Therefore, to obtain the graph of y=f(x)+8 from the graph of f(x) shift the graph of f(x) upwards by 8 units.

(b)

To determine

### To find: The way to obtain the graph of y=f(x+8) with the help of graph of f(x) .

Expert Solution

To obtain the graph of y=f(x+8) from the graph of f(x) shift the graph of f(x) to the left by 8 units.

### Explanation of Solution

Given information:

The graph of f(x) is given.

Calculation:

The graph of function f(x) is given and the function y=f(x+8) takes the value of f(x) to f(x8) .

Shift the graph of f(x) to the left by 8 units for the graph of y=f(x+8) .

Therefore, to obtain the graph of y=f(x+8) from the graph of f(x) shift the graph of f(x) to the left by 8 units.

(c)

To determine

### To find: The way to obtain the graph of y=1+2f(x) with the help of graph of f(x) .

Expert Solution

To obtain the graph of y=1+2f(x) from the graph of f(x) stretch the graph of f(x) vertically by the factor 2 and then shift upward by 1 unit.

### Explanation of Solution

Given information:

The graph of f(x) is given.

Calculation:

The graph of function f(x) is given and the function y=2f(x) doubles the value of f(x) .

So, the graph of 2f(x) is the vertical stretch of graph of f(x) by factor 2 .

Now shift the graph of 2f(x) upwards by 1 unit it gives the graph of function y=1+2f(x) .

Therefore, to obtain the graph of y=1+2f(x) from the graph of f(x) stretch the graph of f(x) vertically by the factor 2 and then shift upward by 1 unit.

(d)

To determine

### To find: The way to obtain the graph of y=f(x−2)−2 with the help of graph of f(x) .

Expert Solution

To obtain the graph of y=f(x2)2 from the graph of f(x) shift the graph of f(x) to the right by 2 units and downwards by 2 units.

### Explanation of Solution

Given information:

The graph of f(x) is given.

Calculation:

Shift the graph of function f(x) by 2 units to the right it gives the graph of function f(x2) .

Now shift the graph of f(x2) downwards by 2 units it gives the graph of function y=f(x2)2 .

Therefore, to obtain the graph of y=f(x2)2 from the graph of f(x) shift the graph of f(x) to the right by 2 units and downwards by 2 units.

(e)

To determine

### To find: The way to obtain the graph of y=f(−x) with the help of graph of f(x) .

Expert Solution

To obtain the graph of y=f(x) from the graph of f(x) reflect it through the y axis.

### Explanation of Solution

Given information:

The graph of f(x) is given.

Calculation:

The graph of the function y=f(x) is the reflection of the graph of function f(x) through the y axis.

Therefore, to obtain the graph of y=f(x) from the graph of f(x) reflect it through the y axis.

(f)

To determine

### To find: The way to obtain the graph of y=−f(−x) with the help of graph of f(x) .

Expert Solution

To obtain the graph of y=f(x) from the graph of f(x) reflect the graph through y axis and then through x axis.

### Explanation of Solution

Given information:

The graph of f(x) is given.

Calculation:

The graph of the function f(x) is the reflection of the graph of function f(x) through the y axis.

Now reflect the graph of f(x) through the x axis it gives the graph of function y=f(x) .

Therefore, to obtain the graph of y=f(x) from the graph of f(x) reflect the graph through y axis and then through x axis.

(g)

To determine

### To find: The way to obtain the graph of y=−f(x) with the help of graph of f(x) .

Expert Solution

To obtain the graph of y=f(x) from the graph of f(x) reflect the graph through x axis.

### Explanation of Solution

Given information:

The graph of f(x) is given.

Calculation:

The graph of the function y=f(x) is the reflection of the graph of function f(x) through the x axis.

Therefore, to obtain the graph of y=f(x) from the graph of f(x) reflect the graph through x axis.

(h)

To determine

### To find: The way to obtain the graph of y=f−1(x) with the help of graph of f(x) .

Expert Solution

To obtain the graph of y=f1(x) from the graph of f(x) reflect it through the line y=x .

### Explanation of Solution

Given information:

The graph of f(x) is given.

Calculation:

The function f1(x) is the inverse of the function f(x) and it is obtained by the reflection of graph of f(x) through the line y=x .

Therefore, to obtain the graph of y=f1(x) from the graph of f(x) reflect it through the line y=x .

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