# To graph: For the given member of family in viewing rectangle indicated.

### 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 2.2, Problem 71E

(a)

To determine

## To graph: For the given member of family in viewing rectangle indicated.

Expert Solution

### Explanation of Solution

Given information:

The given function is f(x)=(xc)3 .

The value of c is c=0,2,4,6;[10,10]by[10,10] .

Graph:

The graph for the given family of equations is shown in figure (1).

Figure (1)

Interpretation: Graph for the family of equations of the function f(x)=(xc)3 is shown in figure (1).

(b)

To determine

Expert Solution

### Explanation of Solution

Given information:

The given function is f(x)=(xc)3 .

The value of c is c=0,2,4,6;[5,5]by[10,10] .

Graph:

The graph for the given family of equations is shown in figure (2).

Figure (2)

Interpretation: Graph for the family of equations of the function f(x)=(xc)3 is shown in figure (2).

(c)

To determine

### To find: The conclusions from the graphs and effects on the value of c .

Expert Solution

All the graphs are the same graph but with different y intercepts.

### Explanation of Solution

Given information:

The given function is f(x)=(xc)3 .

Calculation:

From the graphs in part (a) and (b), we can observe that all the graphs are the same graph but with different y intercepts.

In case when c is less than 0 , then the graph of y=(xc)3 is the same as the graph of y=x3 shifted c units towards left.

In case when |c| is greater than 0 , then the graph of y=(xc)3 is the same as the graph of y=x3 shifted |c| units toward right.

Therefore, all the graphs are the same graph but with different y intercepts.

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