# How do you graph y=(x+2)/(x-3) using asymptotes, intercepts, end behavior?

Nov 29, 2017

here is the graph:

#### Explanation:

To graph $y = \frac{x + 2}{x - 3}$:

$N P V = 3$
There are no common factors between the numerator and denominator so the vertical asymptote is 3.
$V A = 3$

Horizontal Asymptote:
$\mathrm{de} g N = \mathrm{de} g D$

when the numerator and denominator equal the same, you divide the leading coefficients to get the horizontal asymptote.

$H A : y = \frac{x}{x} = 1$

There is no slant asymptote.

Find behaviour near V.A (generally =+/-0.1 away):

at $x = 3.1$ = $\frac{+}{+}$ = positive infinity

at $x = 2.9$ = $\frac{+}{-}$ = negative infinity

so $x = 3.1$ will start to the right of the vertical asymptote in quadrant I, and $x = 2.9$ will start to the left of the vertical asymptote in quadrant IV.

The x intercept is the zero of the numerator, so $x = - 2$
To find the y intercept, set $x = 0$ into the equation.

$y = \frac{0 + 2}{0 - 3}$
$y = \frac{2}{-} 3$ or -0.6667

Join the points smoothly.