# How do you find the asymptotes for y=1/(2-x)?

Feb 16, 2016

$y = 0$
and
$x = 2$

#### Explanation:

As $x \rightarrow \pm \infty$ the $2$ in the denominator becomes less and less significant and
${\lim}_{x \rightarrow \pm \infty} \frac{1}{2 - x} = \frac{1}{\pm \infty} = 0$
Therefore $y = 0$ is an asymptote.

y=1/(2-x is defined for all values up to but not including $x = 2$;
$y \rightarrow \pm \infty$ as $x \rightarrow 2$
Therefore $x = 2$ is an asymptote.

Here is what the graph looks like:
graph{1/(2-x) [-10, 10, -5, 5]}