# How do you find the vertical, horizontal or slant asymptotes for  f(x) = (x+4)/(x-2) ?

Apr 12, 2016

$x = 2$
$y = 1$

#### Explanation:

The equation is undefined when the denominator becomes 0. Consequently the excluded value is $x = 2$ thus there is a vertical asymptote at $x = 2$

As the value of $x$ increases significantly in both the positive and negative domains the influence of the constants of 4 and -2 becomes less and less significant.

Thus ${\lim}_{x \to \pm \infty} \frac{x + 4}{x - 2} \to \frac{x}{x} = 1$

So $y = 1$ is an asymptote.