Chapter 8.3, Problem 13PPS

To determine

To graph the function and state the domain and range.

Explanation of Solution

Given information:

The given function is:

  $f\left(x\right)=\frac{2}{x-6}$

Graph:

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

  $a=2$ : The graph is expanded.

  $h=6$ : The graph is translated $6\text{ units}$ right. There is an asymptote at $x=6$ .

  $k=0$ : There is an asymptote at $f\left(x\right)=0$ .

The graph of the function is:

  

Interpretation:

The domain of the graph is all real numbers not equal to $6$ and the range is all real numbers except $0$ .