Question

How do you find the asymptotes for `f(x)=(1-5x) /( 1+2x)`?

Answer 1

The vertical may be found by setting the lower part `=0`

Explanation:

So you may expect an asymptote at `1+2x=0->x=-1/2`

For the horizontal asymptote we make `x` very large (both pos. and neg.). The function will begin to look more and more like:

`(-5cancelx)/(2cancelx)` as the `1`'s won't make any difference.

So the horizontal asymptote will be `y=-2 1/2`
graph{(1-5x)/(1+2x) [-10, 10, -5, 5]}