Chapter 3.2, Problem 20E

a.

To determine

To describe: the graph of function related to the parent function $f\left(x\right)$ .

Answer to Problem 20E

Graph is stretched vertically by a factor of 1.5 and it will be mirrored by the x-axis.

Explanation of Solution

Given information:

  $\begin{array}{c}f\left(x\right)=x^2\\ y=-{\left(1.5x\right)}^2\end{array}$

Calculation:

Since the function is multiplied by 1.5, so the graph is stretch vertically by a factor of 1.5. As it is also multiplied by $-1$ , this means that the graph will be mirrored by the x-axis.

b.

To determine

To describe: the graph of function related to the parent function $f\left(x\right)$ .

Answer to Problem 20E

The graph is stretched vertically by a factor of 4 and it is shifted right by 3 units.

Explanation of Solution

Given information:

  $\begin{array}{c}f\left(x\right)=x^2\\ y=4{\left(x-3\right)}^2\end{array}$

Calculation:

Since x is replaced with $\left(x-3\right)$ , so it is first shifted three units to the right and then it is multiplied by 4, so it will be stretched vertically by a factor of 4.

c.

To determine

To describe: the graph of function related to the parent function $f\left(x\right)$ .

Answer to Problem 20E

The graph is compressed vertically by a factor of $\frac{1}{2}$ and it is shifted downwards by 5 units.

Explanation of Solution

Given information:

  $\begin{array}{c}f\left(x\right)=x^2\\ y=\frac{1}{2}{x}^2-5\end{array}$

Calculation:

First x is multiplied by $\frac{1}{2}$ , so the graph will be compressed vertically by a factor of $\frac{1}{2}$ and then 5 is subtracted to the function, which means it is shifted downwards by 5 units.