Chapter 9.4, Problem 17PPS

To determine

To graph: The given function.

Explanation of Solution

Given information:

The following function:

  $f\left(x\right)=\frac{1}{{(x+4)}^2}$

Calculation:

Step 1:

Find the zeroes.

Since $a(x)=1$ , there are no zeroes.

Step 2:

Find the asymptotes.

  $\begin{array}{l}$ {(x+4)}^2=0[\text{Set }b(x)=0]$x+4=0[\text{Take square root of each side]}\\ x=-4[\text{Subtract 4 from each side]}\end{array}$

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

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: