Chapter 3.6, Problem 4Q

Solution

To Graph: The function $y=-\frac{1}{2}\sqrt[3]{x}$ and also state the domain and range.

Given information:

The function is $y=-\frac{1}{2}\sqrt[3]{x}$ .

Graph:

For drawing the graph first find the coordinates with the help of the given function.

Substitute the values of x into the function $y=-\frac{1}{2}\sqrt[3]{x}$ to find the values of y ,

Now Put $x=-4$ into $y=-\frac{1}{2}\sqrt[3]{x}$ ,

  $\begin{array}{l}y=-\frac{1}{2}\sqrt[3]{-4}\\ y=0.79\end{array}$

Now substitute $x=0$ into $y=-\frac{1}{2}\sqrt[3]{x}$ ,

  $\begin{array}{l}y=-\frac{1}{2}\sqrt[3]{0}\\ y=0\end{array}$

Now substitute $x=4$ into $y=-\frac{1}{2}\sqrt[3]{x}$ ,

  $\begin{array}{l}y=-\frac{1}{2}\sqrt[3]{4}\\ y=-0.79\end{array}$

The resultant table is:

X	$y=-\frac{1}{2}\sqrt[3]{x}$
$-4$	$0.79$
0	0
4	$-0.79$
8	$-1$

Now consider the above table and draw the graph:

  

Interpretation: The graph of equation $y=-\frac{1}{2}\sqrt[3]{x}$ is passing through the points $\left(-4,0.79\right),\left(0,0\right),\left(4,-0.79\right)\text{and}\left(8,-1\right)$ .

The domain of the function $y=-\frac{1}{2}\sqrt[3]{x}$ is all real numbers and the range of the function is all set of real numbers.