Chapter 5.2, Problem 17E

Solution

To graph: The function $y=\frac{-3}{x+2}$ and its domain and range.

Given information:

The function $y=\frac{-3}{x+2}$.

Graph:

The given function is in form of $f\left(x\right)=\frac{a}{x-h}+k$ , where $a=-3,h=-2,\text{ and }k=0$.

The asymptotes of $f\left(x\right)=\frac{a}{x-h}+k$ will be $x=h,y=k$.

The asymptote of the given function is $x=-2,y=0$.

Make a table to find some points on the graph that are to the left and right of the vertical asymptote.

$x$	$-1$	$-3$	$-5$	$1$
$y=\frac{-3}{x+2}$	$-1$	$3$	$1$	$-1$

Draw the graph of the given function.

  

Domain is the set of $x-$ values and range is the set of $y-$ values.

From the graph it can be observed that all real values except $-2$ are in the set of $x-$ values and all real values except $0$ are in the set of $y-$ values.

Interpretation:

The domain of the given function is the set of all real values other than $-2$ and range is the set of all real values other than $0$.