# How do you graph y=(x+4)/(x-3) using asymptotes, intercepts, end behavior?

Jan 11, 2018

See below.

#### Explanation:

$y = \frac{x + 4}{x - 3}$

This is undefined at $x = 3$, so vertical asymptote occurs here.

$\frac{x + 4}{x - 3}$

Divide by $x$

$\frac{\frac{x}{x} + \frac{4}{x}}{\frac{x}{x} - \frac{3}{x}} = \frac{1 + \frac{4}{x}}{1 - \frac{3}{x}}$

as $x \to \infty \textcolor{w h i t e}{88888}$ , $\frac{1 + \frac{4}{x}}{1 - \frac{3}{x}} = \frac{1 + 0}{1 - 0} = 1$

as $x \to - \infty \textcolor{w h i t e}{888}$ , $\frac{1 + \frac{4}{x}}{1 - \frac{3}{x}} = \frac{1 + 0}{1 - 0} = 1$

$\therefore$

$y = 1$ is a horizontal asymptote.

GRAPH: