Exercise 17 Page 526

We are asked to graph the given function. Then we will state the domain and the range.

Graph

To graph the function, we will make a table of positive and negative values. Note that $x$ cannot be zero because division by zero is not defined.

$x$	$\frac{\text{-}2}{x}$	$y=\frac{\text{-}2}{x}$
$0.25$	$\frac{\text{-}2}{0.25}$	$\text{-}8$
$0.5$	$\frac{\text{-}2}{0.5}$	$\text{-}4$
$1$	$\frac{\text{-}2}{1}$	$\text{-}2$
$2$	$\frac{\text{-}2}{2}$	$\text{-}1$
$8$	$\frac{\text{-}2}{8}$	$\text{-}0.25$
$\text{-}0.25$	$\frac{\text{-}2}{\text{-}0.25}$	$8$
$\text{-}0.5$	$\frac{\text{-}2}{\text{-}0.5}$	$4$
$\text{-}1$	$\frac{\text{-}2}{\text{-}1}$	$2$
$\text{-}2$	$\frac{\text{-}2}{\text{-}2}$	$1$
$\text{-}8$	$\frac{\text{-}2}{\text{-}8}$	$0.25$

Because $x$ cannot be zero the graph will not cross the $y\text{-}$axis. Therefore, we need two curves to connect the points.

Domain and Range

Consider the given function. Since the denominator cannot be $0,$ $x$ cannot be $0.$ The domain of the function is all real numbers except $0.$ Moreover, the numerator is never $0,$ so $y$ is never $0.$ The range is all real numbers except $0.$