Chapter 1.7, Problem 10E

a.

To determine

To plot: Graph $y=f\left(x-5\right)$ as per given graph.

Answer to Problem 10E

The function shifts horizontally $5units$ right. The required diagram is shown in Figure 1

Explanation of Solution

Given information:

Given,

  

Calculation:

Consider the function,

  $y=f\left(x-5\right)$

The graph of the function shifts horizontally $5units$ right.

The sketch for the graph is shown in Figure 1

  

Figure 1

b.

To determine

To plot: Graph $y=-f\left(x\right)+3$ as per given graph.

Answer to Problem 10E

Invert the given graph of function with respect to $x-axis$ , then shift the graph $3units$ upward. The required diagram is shown in Figure 2

Explanation of Solution

Given information:

Given,

  

Calculation:

Consider the function,

  $y=-f\left(x\right)+3$

Invert the given graph of function with respect to $x-axis$ , then shift the graph $3units$ upward.

The sketch for the graph is shown in Figure 1

  

Figure 2

c.

To determine

To plot: Graph $y=\frac{1}{3}f\left(x\right)$ as per given graph.

Answer to Problem 10E

Reduce the amplitude of graph of function by $\frac{1}{3}units$ . The required diagram is shown in Figure 3.

Explanation of Solution

Given information:

Given,

  

Calculation:

Consider the function,

  $y=\frac{1}{3}f\left(x\right)$

Reduce the amplitude of graph of function by $\frac{1}{3}units$ .

The sketch for the graph is shown in Figure 3

  

Figure 3

d.

To determine

To plot: Graph $y=-f\left(x+1\right)$ as per given graph.

Answer to Problem 10E

Invert the graph of function with respect to $x-axis$ then shifts horizontally $1unit$ left. The required diagram is shown in Figure 4

Explanation of Solution

Given information:

Given,

  

Calculation:

Consider the function,

  $y=-f\left(x+1\right)$

Invert the graph of function with respect to $x-axis$ then shifts horizontally $1unit$ left.

The sketch for the graph is shown in Figure 4

  

Table 4

e.

To determine

To plot: Graph $y=f\left(-x\right)$ as per given graph.

Answer to Problem 10E

The required diagram is shown in Figure 5.

Explanation of Solution

Given information:

Given,

  

Calculation:

Consider the function,

  $y=f\left(-x\right)$

Invert the graph of function with respect to $y-axis$ .

The sketch for the graph is shown in Figure 5

  

Figure 5

f.

To determine

To plot: Graph $y=f\left(x\right)-10$ as per given graph.

Answer to Problem 10E

Shifts the graph of function vertically $10units$ below. The required diagram is shown in Figure 6.

Explanation of Solution

Given information:

Given,

  

Calculation:

Consider the function,

  $y=f\left(x\right)-10$

Shifts the graph of function vertically $10units$ below.

The sketch for the graph is shown in Figure 6

  

Figure 6

g.

To determine

To plot: Graph $y=f\left(\frac{1}{3}x\right)$ as per given graph.

Answer to Problem 10E

Shifts the graph of function vertically $10units$ below. The required diagram is shown in Figure 7

Explanation of Solution

Given information:

Given,

  

Calculation:

Consider the function,

  $y=f\left(\frac{1}{3}x\right)$

Shrinks the graph of function $\frac{1}{3}units$ about the $x-axis$ .

The sketch for the graph is shown in Figure 7

  

Figure 7