Question

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

Answer 1

`y=0`
and
`x=2`

Explanation:

As `xrarr+-oo` the `2` in the denominator becomes less and less significant and
`lim_(xrarr+-oo) 1/(2-x) = 1/(+-oo) = 0`
Therefore `y=0` is an asymptote.

`y=1/(2-x` is defined for all values up to but not including `x=2`;
`yrarr +-oo` as `xrarr2`
Therefore `x=2` is an asymptote.

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