Question

How to find the asymptotes of `f(x) = 6^(x-2)`?

Answer 1

`y=0`

Explanation:

Find the limit in either infinite direction.

`lim_(xrarroo)6^(x-2)=6^oo=oo`

`lim_(xrarr-oo)6^(x-2)=6^-oo=1/6^oo=0`

Note that this is just a mental process to undergo.

Thus the asymptote is `y=0` (as `xrarr-oo)`.

We can check a graph:

graph{6^(x-2) [-8.535, 13.965, -2.52, 8.73]}