# How do you find the domain and range of y=1/(x-4)?

##### 1 Answer
Jun 25, 2015

The only restriction on the domain is $x \ne 4$
As this would make the numerator $= 0$

#### Explanation:

As $x$ nears $4$ from above, $y$ will be larger and larger, or in "the language":
${\lim}_{x \to 4 +} y = \infty$
Something like that goes if $x$ nears $4$ from below:
${\lim}_{x \to 4 -} y = - \infty$
$x = 4$ is called the vertical asymptote.

$y$ can never reach the value of $0$ ( horizontal asymptote), so th range is $y \ne 0$, or:
${\lim}_{x \to \infty} y = 0$

graph{1/(x-4) [-5.04, 14.96, -4.24, 5.76]}