Chapter 1.7, Problem 58E

(a)

To determine

To find: The function for the given graph.

Answer to Problem 58E

The required function is $f\left(x\right)=8\sqrt{x}$ .

Explanation of Solution

Given:

The given function is $f\left(x\right)=\sqrt{x}$ .

The given graph is shown in Figure 1

  

Figure 1

Calculation:

The general form for the equation of the graph is,

  $f\left(x\right)=a\sqrt{x}+b$

The equation of the graph for the points $\left(4,16\right)$ is,

  $\begin{array}{c}16=a\sqrt{4}+b\\ =2a+b\end{array}$

The equation of the graph for the points $\left(0,0\right)$ is,

  $\begin{array}{l}0=a\sqrt{0}+b\\ b=0\end{array}$

Then,

  $\begin{array}{l}16=a\sqrt{4}+0\\ a=8\end{array}$

Then, the equation of the graph is,

  $\begin{array}{c}f\left(x\right)=8\sqrt{x}+0\\ =8\sqrt{x}\end{array}$

(b)

To determine

To find: The function for the given graph.

Answer to Problem 58E

The required function is $f\left(x\right)=\frac{-1}{4}\sqrt{x}$ .

Explanation of Solution

Given:

The given function is $f\left(x\right)=\sqrt{x}$ .

The given graph is shown in Figure 2

  

Figure 2

Calculation:

The general form for the equation of the graph is,

  $f\left(x\right)=a\sqrt{x}+b$

The equation of the graph for the points $\left(4,-\frac{1}{2}\right)$ is,

  $\begin{array}{c}-\frac{1}{2}=a\sqrt{4}+b\\ =2a+b\end{array}$

The equation of the graph for the points $\left(0,0\right)$ is,

  $\begin{array}{l}0=a\sqrt{0}+b\\ b=0\end{array}$

Then,

  $\begin{array}{l}-\frac{1}{2}=a\sqrt{4}+0\\ a=\frac{-1}{4}\end{array}$

Then, the equation of the graph is,

  $f\left(x\right)=\frac{-1}{4}\sqrt{x}$