Chapter 3.5, Problem 9E

Solution

The graph of the function shown in the given options:

  

The given graph is of the function $y=-\frac{3}{2}\sqrt{x}$ .

Given:

The options given are as follow:

  $\begin{array}{l}\left(\text{A}\right)y=\frac{3}{4}\sqrt{x}\\ \left(\text{B}\right)y=-\frac{3}{4}\sqrt{x}\\ \left(\text{C}\right)y=\frac{3}{2}\sqrt{x}\\ \left(\text{D}\right)y=-\frac{3}{2}\sqrt{x}\end{array}$

Calculation:

In the given graph, the value of the function is $-3$ at $x=4$ :

Evaluate the function $y=\frac{3}{4}\sqrt{x}$ for $x=4$ which should give a result of $-3$ :

  $\begin{array}{l}y=\frac{3}{4}\sqrt{4}\left[\text{Substitute}\text{4}\text{for}\text{x}\right]\\ \Rightarrow =\frac{3}{2}\end{array}$

Since the value of the function for $x=4$ is not equivalent to $-3$ , option $\left(\text{A}\right)$ is incorrect.

Evaluate the function $y=-\frac{3}{4}\sqrt{x}$ for $x=4$ which should give a result of $-3$ :

  $\begin{array}{l}y=-\frac{3}{4}\sqrt{4}\left[\text{Substitute}\text{4}\text{for}\text{x}\right]\\ \Rightarrow =-\frac{3}{2}\end{array}$

Since the value of the function for $x=4$ is not equivalent to $-3$ , option $\left(\text{B}\right)$ is incorrect.

Evaluate the function $\text{y=}\frac{3}{2}\sqrt{x}$ for $x=4$ which should give a result of $-3$ :

  $\begin{array}{l}\text{y=}\frac{3}{2}\sqrt{x}\left[\text{Substitute}\text{4}\text{for}x\right]\\ \Rightarrow =3\end{array}$

Since the value of the function for $x=4$ is not equivalent to $-3$ , option $\left(\text{C}\right)$ is incorrect.

Evaluate the function $\text{y=-}\frac{3}{2}\sqrt{x}$ for $x=4$ which should give a result of $-3$ :

  $\begin{array}{l}\text{y=-}\frac{3}{2}\sqrt{x}\left[\text{Substitute}\text{4}\text{for}x\right]\\ \Rightarrow =-3\end{array}$

Since the value of the function for $x=4$ is equivalent to $-3$ , option $\left(\text{D}\right)$ is incorrect.

Hence, the only correct option is $\left(\text{D}\right)$ .