Chapter 1.7, Problem 9E

(a)

To determine

To graph: The function $y=f\left(-x\right)$

Explanation of Solution

Given information:

The given function is $y=f\left(-x\right)$ is given as figure.

  

Graph:

Consider the function $y=f\left(-x\right)$ ,reflect the graph of $y=f\left(x\right)$ in the y-axis as shown in figure-(1).

  

Figure-(1)

Interpretation: Graph for the functions $y=f\left(-x\right)$ shows in figure (1).

(b)

To determine

To graph: The function $y=f\left(x\right)+4$ .

Explanation of Solution

Given information:

The given function is $y=f\left(x\right)+4$

Graph:

Consider the function $y=f\left(x\right)+4$ ,shift the graph of $y=f\left(x\right)$ 4 units upward as shown in figure(1).

  

Figure-(1)

Interpretation: Graph for the functions $y=f\left(x\right)+4$ shows in figure (1).

(c)

To determine

To graph: The function $y=2f\left(x\right)$ .

Explanation of Solution

Given information:

The given function is $y=2f\left(x\right)$

Graph:

Consider the function $y=2f\left(x\right)$ ,sketch the graph of $y=f\left(x\right)$ vertically by 2 units as shown in figure(1).

  

Figure-(1)

Interpretation: Graph for the functions $y=2f\left(x\right)$ shows in figure (1).

(d)

To determine

To graph: The function $y=-f\left(x-4\right)$.

Explanation of Solution

Given information:

The given function is $y=-f\left(x-4\right)$

Graph:

Consider the function $y=-f\left(x-4\right)$ ,sketch the graph of $y=f\left(x\right)$ to the right 4units, and then reflect it in the x-axis as shown in figure(1).

  

Figure-(1)

Interpretation: Graph for the functions $y=-f\left(x-4\right)$ shows in figure (1).

(e)

To determine

To graph: The function $y=f\left(x\right)-3$ .

Explanation of Solution

Given information:

The given function is $y=f\left(x\right)-3$

Graph:

Consider the function $y=f\left(x\right)-3$ ,sketch the graph of $y=f\left(x\right)$ 3 units downward as shown in figure(1).

  

Figure-(1)

Interpretation: Graph for the functions $y=f\left(x\right)-3$ shows in figure (1).

(f)

To determine

To graph: The function $y=-f\left(x\right)-1$ .

Explanation of Solution

Given information:

The given function is $y=-f\left(x\right)-1$

Graph:

Consider the function $y=-f\left(x\right)-1$ ,sketch the graph of $y=f\left(x\right)$ in the x-axis, and then shift it 1 unit downward as shown in figure(1).

  

Figure-(1)

Interpretation: Graph for the functions $y=-f\left(x\right)-1$ shows in figure (1).

(g)

To determine

To graph: The function $y=f\left(2x\right)$ .

Explanation of Solution

Given information:

The given function is $y=f\left(2x\right)$

Graph:

Consider the function $y=f\left(2x\right)$ ,sketch the graph of $y=f\left(x\right)$ vertically by 2 units as shown in figure(1).

  

Figure-(1)

Interpretation: Graph for the functions $y=f\left(2x\right)$ shows in figure (1).