Chapter 9.4, Problem 13PPS

To determine

To graph: The given function.

Explanation of Solution

Given information:

The following function:

  $f\left(x\right)=\frac{x}{x+2}$

Calculation:

Step 1:

Find the zeroes.

  $x=0[\text{Set }a(x)=0]$

There is a zero at $x=0$ .

Step 2:

Find the asymptotes.

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

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

The degree of numerator is equal to the degree of the denominator.

Therefore, the horizontal asymptote is the line:

  $\begin{array}{l}y=\frac{\text{leading coefficient of }a(x)}{\text{leading of coefficient of }b(x)}\\ y=\frac{1}{1}=1\text{ [Set leading coefficient of }a(x)=1\text{ and }\\ \text{ the leading of coefficient of }b(x)=1]\end{array}$

There is a horizontal asymptote at $y=1$ .

Step 3:

Draw the graph

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

The table of values:

  

The graph: