Chapter 9.4, Problem 2CYU

To determine

To graph: The given function.

Explanation of Solution

Given information:

The following function:

  $f\left(x\right)=\frac{x^3}{x+2}$ .

Calculation:

Step 1:

Find the zeroes.

  $\begin{array}{l}{x}^3=0[\text{Set }a(x)=0]\\ x=0[\text{Find cube root of both sides]}\end{array}$

There is a zero at $x=0$ .

Step 2:

Find the asymptotes.

  $\begin{array}{l}x+2=0[\text{Set }b(x)=0]\\ x=-2[\text{Subtract 2 from both sides]}\end{array}$

There is a vertical asymptote at $x=-2$ .

The degree of numerator is greater than the degree of the denominator.

So, there is no horizontal asymptote.

Step 3:

Draw the graph

Use a table to find ordered pairs on the graph. Then connect the points