Chapter 9.4, Problem 14PPS

To determine

To graph: The given function.

Explanation of Solution

Given information:

The following function:

  $f\left(x\right)=\frac{5}{(x-1)(x+4)}$

Calculation:

Step 1:

Find the zeroes.

Since $a(x)=5$ , there are no zeroes.

Step 2:

Find the asymptotes.

  $\begin{array}{l}(x-1)(x+4)=0[\text{Set }b(x)=0]\\ x-1=0\text{ or }x+4=0[\text{Set each factor to 0]}\\ x=1\text{ and }x=-4[\text{Simplify]}\end{array}$

There is a vertical asymptote at $x=1$ and $x=-4$ .

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

Therefore, the horizontal asymptote is the line $f(x)=0$ .

The difference between the degree of the numerator and the degree of the denominator is $2$ , so there no oblique asymptote.

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: