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

Feb 19, 2016

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

#### Explanation:

So you may expect an asymptote at $1 + 2 x = 0 \to x = - \frac{1}{2}$

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

$\frac{- 5 \cancel{x}}{2 \cancel{x}}$ as the $1$'s won't make any difference.

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