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.

$x$	$\frac{- 2}{x}$	$y = \frac{- 2}{x}$
$0.25$	$\frac{- 2}{0 . 2 5}$	$- 8$
$0.5$	$\frac{- 2}{0 . 5}$	$- 4$
$1$	$\frac{- 2}{1}$	$- 2$
$2$	$\frac{- 2}{2}$	$- 1$
$8$	$\frac{- 2}{8}$	$- 0.25$
$- 0.25$	$\frac{- 2}{- 0 . 2 5}$	$8$
$- 0.5$	$\frac{- 2}{- 0 . 5}$	$4$
$- 1$	$\frac{- 2}{- 1}$	$2$
$- 2$	$\frac{- 2}{- 2}$	$1$
$- 8$	$\frac{- 2}{- 8}$	$0.25$

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

Domain and Range

Consider the given function.

y = \frac{- 2}{x}

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 .

Domain : Range : All real numbers except x = 0 All real numbers except y = 0

Exercise