Chapter 3.6, Problem 5Q

Solution

To Graph: The function $f\left(x\right)=\sqrt[3]{x}-4$ and also state the domain and range.

Given information:

The function is $f\left(x\right)=\sqrt[3]{x}-4$ .

Graph:

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

Let’s take $y=f\left(x\right)$

Substitute the values of x into the function $y=\sqrt[3]{x}-4$ to find the values of y ,

Now Put $x=-8$ into $y=\sqrt[3]{x}-4$ ,

  $\begin{array}{l}y=\sqrt[3]{-8}-4\\ y=-6\end{array}$

Now substitute $x=0$ into $y=\sqrt[3]{x}-4$ ,

  $\begin{array}{l}y=\sqrt[3]{0}-4\\ y=-4\end{array}$

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

  $\begin{array}{l}y=\sqrt[3]{2}-4\\ y=-2.7\end{array}$

The resultant table is:

x	$y=\sqrt[3]{x}-4$
$-8$	$-6$
$-2$	$-5.3$
0	$-4$
2	$-2.7$
8	$-2$

Now consider the above table and draw the graph:

  

Interpretation: The graph of equation $f\left(x\right)=\sqrt[3]{x}-4$ is passing through the points $\left(-8,-6\right),\left(0,0\right),\left(2,-2.7\right)\text{and}\left(8,-2\right)$ .

The domain of the function $f\left(x\right)=\sqrt[3]{x}-4$ is all real numbers and the range of the function is all set of real numbers.