Chapter 3.2, Problem 23E

a.

To determine

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

Answer to Problem 23E

Graph is shifted to left by 2 units and it is compressed vertically by the factor of $\frac{1}{3}$ .

Explanation of Solution

Given information:

  $\begin{array}{c}f\left(x\right)=\sqrt{x}\\ y=\frac{1}{3}\sqrt{x+2}\end{array}$

Calculation:

Since x is first replaced with $\left(x+2\right)$ , so the graph is shifted to the left by 2 units and then the function is then multiplied by $\frac{1}{3}$ , which means that then graph will be compressed vertically by a factor of $\frac{1}{3}$ .

b.

To determine

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

Answer to Problem 23E

The graph is mirrored along y-axis and is shifted downwards by 7 units.

Explanation of Solution

Given information:

  $\begin{array}{c}f\left(x\right)=\sqrt{x}\\ y=\sqrt{-x}-7\end{array}$

Calculation:

Since x is multiplied by $\left(-1\right)$ , so the graph is mirrored along y-axis and then the function is subtraced by 7, so it is shifted downwards by 7 units.

c.

To determine

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

Answer to Problem 23E

The graph is shifted upward to right side and is stretched vertically.

Explanation of Solution

Given information:

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

Calculation:

First x is replaced with $\left(x-3\right)$ , so the graph is shifted to the right by 3 units. The function is then multiplied by 2, so it is stretched vertically by a factor of 2 and 4 is added to the function so it is shifted upwards by 4 units.