Chapter 8.3, Problem 19PPS

To determine

To graph the function and state the domain and range.

Explanation of Solution

Given information:

The given function is:

  $f\left(x\right)=\frac{9}{x+3}+6$

Graph:

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

  $a=9$ : The graph is expanded.

  $h=-3$ : The graph is translated $3\text{ units}$ left. There is an asymptote at $x=-3$ .

  $k=6$ : The graph is translated $\text{6 units}$ up. There is an asymptote at $f\left(x\right)=6$ .

The graph of the function is:

  

Interpretation:

The domain of the graph is all real numbers not equal to $-3$ and the range is all real numbers except $6$ .