# How do you find the vertical, horizontal or slant asymptotes for y = 3/(x + 4)?

May 31, 2016

Vertical asymptote is $x = - 4$
Horizontal asymptote is $y = 0$

#### Explanation:

The equation is undefined at $x = - 4$ as $\frac{1}{x - 4} \to \frac{1}{0}$ and division by 0 'is not allowed'. So excluded value is $x = - 4$

This $x = - 4$ is a vertical asymptote.
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

As the magnitude of $x$ increases in both the positive and negative directions then $| x + 4 |$ becomes so large that $\frac{3}{x + 4}$ becomes exceptionally small.

Thus

${\lim}_{x \to - 4} \frac{3}{x + 4} = \pm 0$