Chapter 13.5, Problem 83S

To determine

To graph : The given graph is $f(x)=\frac{x+2}{x^2-x-6}$ .

Explanation of Solution

Given information :

We know that, the given information is $f(x)=\frac{x+2}{x^2-x-6}$ .

Calculation :

The given equation is

  $\begin{array}{l}{x}^2-x-6=x^2-3x+2x-6\\ =x(x-3)+2(x-3)\\ =(x-3)(x+2)\\ f(x)=\frac{x+2}{(x-3)(x+2)}=\frac{1}{x-3},x\ne -2\end{array}$

Graph :

  

Interpretation :

  $\begin{array}{l}Asx\to 3\text{graph approaches +}\infty \text{ or –}\infty \text{.}\\ \text{and x}\to \infty \text{ graph approaches zero}\text{.}\\ \text{or x}\to –\infty \text{ graph approaches zero}\text{.}\end{array}$