Chapter 9.3, Problem 5CYU

To determine

To graph the function and state the domain and range.

Explanation of Solution

Given information:

The given function is:

  $f\left(x\right)=\frac{-1}{x-2}+4$

Graph:

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

  $a=-1$ : The graph is expanded and reflected across the x-axis.

  $h=2$ : The graph is translated $2\text{ units}$ right. There is an asymptote at $x=2$ .

  $k=4$ : The graph is translated $4\text{ units}$ up. There is an asymptote at $f\left(x\right)=4$ .

The graph of the function is:

  

Interpretation:

The domain of the graph is all real numbers not equal to $2$ and the range is all real numbers except $4$ .