Chapter 9.3, Problem 34PPS

To determine

To graph the function and state the domain, range, and the asymptotes.

Explanation of Solution

Given information:

The given function is:

  $f\left(x\right)=\frac{-7}{x-8}-9$

Graph:

This represents a transformation of the graph of $f\left(x\right)=\frac{1}{x}$ .

  $a=-7$ : The graph is expanded and translated along the x-axis.

  $h=8$ : The graph is translated $8\text{ units}$ right. There is an asymptote at $x=8$ .

  $k=-9$ : The graph is translated $9\text{ units}$ down. There is an asymptote at $f\left(x\right)=-9$ .

The graph of the function is:

  

Interpretation:

The asymptotes are $x=8\text{ and }f\left(x\right)=-9$ .

The domain of the graph is all real numbers not equal to $8$ and the range is all real numbers except $-9$ .