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

Feb 2, 2017

$y = - \frac{5}{2}$

$x = - \frac{1}{2}$

#### Explanation:

Firstly, find what $x$ cannot be for the vertical asymptotes

So the denominator of the fraction cannot be equal to $0$.

$1 + 2 x \ne 0$
$x \ne - 0.5$

Meaning that $x = - 0.5$ is the vertical asymptote.

Then, find the horizontal/slant asymptotes by only looking at the highest degree of $x$.

$f \left(x\right) = \frac{1 - 5 x}{1 + 2 x}$

As $x \rightarrow \infty$, we only care about the values that will change the function most, so we can just look at the highest degree of $x$. Thus, he asymptote will be:

$y = \frac{- 5 x}{2 x}$

$y = - \frac{5}{2}$