Chapter 1, Problem 11PS

(a)

To determine

To Sketch: The graph for the function $H\left(x\right)-2$ .

Answer to Problem 11PS

The Required sketch is shown in Figure 2

Explanation of Solution

Given:

The given function is $H\left(x\right)-2$ .

Calculation:

The graph for the Heave side function is shown in Figure 1

  

Figure 1

For the graph of the function $H\left(x\right)-2$ the graph is shifted downward $2$ units from the graph of $H\left(x\right)$ .

The required graph is shown in Figure 2

  

Figure 2

(b)

To determine

To Sketch: The graph for the function $H\left(x-2\right)$ .

Answer to Problem 11PS

The Required sketch is shown in Figure 3

Explanation of Solution

Given:

The given function is $H\left(x-2\right)$ .

Calculation:

For the graph of the function $H\left(x-2\right)$ the graph is shifted rightby $2$ units from the graph of $H\left(x\right)$ .

The required graph is shown in Figure 3

  

Figure 3

(c)

To determine

To Sketch: The graph for the function $-H\left(x\right)$ .

Answer to Problem 11PS

The Required sketch is shown in Figure 4

Explanation of Solution

Given:

The given function is $-H\left(x\right)$ .

Calculation:

For the graph of the function $-H\left(x\right)$ is the reflection of the graph of $H\left(x\right)$ .

The required graph is shown in Figure 4

  

Figure 4

(d)

To determine

To Sketch: The graph for the function $H\left(-x\right)$ .

Answer to Problem 11PS

The required sketch is shown in Figure 5

Explanation of Solution

Given:

The given function is $H\left(-x\right)$ .

Calculation:

For the graph of the function $H\left(-x\right)$ is the refraction in the $y$ axisof the graph $H\left(x\right)$ .

The required graph is shown in Figure 5

  

Figure 5

(e)

To determine

To Sketch: The graph for the function $\frac{1}{2}H\left(x\right)$ .

Answer to Problem 11PS

The required sketch is shown in Figure 6

Explanation of Solution

Given:

The given function is $\frac{1}{2}H\left(x\right)$ .

Calculation:

For the graph of the function $\frac{1}{2}H\left(x\right)$ is the vertical shrink of the half of the graph of $H\left(x\right)$ .

The required graph is shown in Figure 6

  

Figure 6

(f)

To determine

To Sketch: The graph for the function $-H\left(x-2\right)+2$ .

Answer to Problem 11PS

The required sketch is shown in Figure 7

Explanation of Solution

Given:

The given function is $-H\left(x-2\right)+2$ .

Calculation:

For the graph of the function $-H\left(x-2\right)+2$ is obtained by shifting the graph $H\left(x\right)$ horizontally 2 unit to the right that is $H\left(x-2\right)$ , then refracting the graph along the y axis that is $-H\left(x-2\right)$ .

Then shifting the graph vertically upward $-H\left(x-2\right)+2$ .

The required graph is shown in Figure 6

  

Figure 7