Chapter 11.4, Problem 73E

(a)

To determine

To find: The graph of $\mathrm{y}$ for each of the transformation on the same rectangular coordinate system also the required graph is shown in Figure 1

Answer to Problem 73E

The function is obtained $\mathrm{x}+3$ for $\mathrm{x}$ in the above equation.

Explanation of Solution

Given Data:

The given expression is $\mathrm{y}={\mathrm{x}}^4$ and the function is $\mathrm{f}\left(\mathrm{x}\right)={\left(\mathrm{x}+3\right)}^4$ .

Calculation:

Consider the given equation is,

  $\mathrm{y}={\mathrm{x}}^4$

Replace $\mathrm{x}+3$ for $\mathrm{x}$ in the above equation.

  $\mathrm{f}\left(\mathrm{x}\right)={\left(\mathrm{x}+3\right)}^4$

(b)

To determine

To find: The graph of $\mathrm{y}$ for each of the transformation on the same rectangular coordinate system also the required graph is shown in Figure 1

Answer to Problem 73E

The function is obtained by shifting the original one unit to the left.

Explanation of Solution

Given Data:

The given expression is $\mathrm{y}={\mathrm{x}}^4$ and the function is $\mathrm{f}\left(\mathrm{x}\right)={\mathrm{x}}^4-1$ .

Calculation:

Consider the given equation is,

  $\mathrm{y}={\mathrm{x}}^4$

Shift the above function one unit to the left as,

  $\mathrm{f}\left(\mathrm{x}\right)={\mathrm{x}}^4-1$

(c)

To determine

To find: The graph of $\mathrm{y}$ for each of the transformation on the same rectangular coordinate system also the required graph is shown in Figure 1

Answer to Problem 73E

The function is obtained by shifting the original two unit to the left.

Explanation of Solution

Given Data:

The given expression is $\mathrm{y}={\mathrm{x}}^4$ and the function is $\mathrm{f}\left(\mathrm{x}\right)=-2+{\mathrm{x}}^4$ .

Calculation:

Consider the given equation is,

  $\mathrm{y}={\mathrm{x}}^4$

Shift the above function two unit to the left as,

  $\mathrm{f}\left(\mathrm{x}\right)={\mathrm{x}}^4-2$

(d)

To determine

To find: The graph of $\mathrm{y}$ for each of the transformation on the same rectangular coordinate system.

Answer to Problem 73E

The function is obtained by shifting the original four unit to the left and scale it by half unit also the required graph is shown in Figure 1

Explanation of Solution

Given Data:

The given expression is $\mathrm{y}={\mathrm{x}}^4$ and the function is $\mathrm{f}\left(\mathrm{x}\right)=\frac{1}{2}{\left(\mathrm{x}-4\right)}^4$ .

Calculation:

Consider the given equation is,

  $\mathrm{y}={\mathrm{x}}^4$

Shift the above function four unit to the left and scale it by half unit

  $\mathrm{f}\left(\mathrm{x}\right)=\frac{1}{2}{\left(\mathrm{x}-4\right)}^4$

The graph is shown in Figure 1

  

Figure 1