Chapter 8.4, Problem 1AGP

To determine

To graph: The given function.

Explanation of Solution

Given information:

The following function:

  $f\left(x\right)=\frac{x^2-x-6}{x+1}$ .

Calculation:

Step 1:

Find the zeroes.

  $\begin{array}{l}{x}^2-x-6=0[\text{Set }a(x)=0]\\ (x+2)(x-3)=0[\text{Factor]}\\ x+2=0x-3=0[\text{Set each factor to 0]}\\ x=-2x=3[\text{Simplify]}\end{array}$

There is a zero at $x=-2$ and $x=3$ .

Step 2:

Find the asymptotes.

  $\begin{array}{l}x+1=0[\text{Set }b(x)=0]\\ x=-1[\text{Subtract 1 from both sides]}\end{array}$

There is a vertical asymptote at

  $x=-1$ .

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