# How to find the asymptotes of y=22/(x+13)-10?

Mar 2, 2017

$\text{vertical asymptote at } x = - 13$
$\text{horizontal asymptote at } y = - 10$

#### Explanation:

The denominator of y cannot be zero as this would make y undefined. Equating the denominator to zero and solving gives the value that x cannot be and if the numerator is non-zero for this value then it is a vertical asymptote.

$\text{solve "x+13=0rArrx=-13" is the asymptote}$

Horizontal asymptotes occur as

${\lim}_{x \to \pm \infty} , y \to c \text{ ( a constant)}$

divide terms on numerator/denominator by x

$y = \frac{\frac{22}{x}}{\frac{x}{x} + \frac{13}{x}} - 10 = \frac{\frac{22}{x}}{1 + \frac{13}{x}} - 10$

as $x \to \pm \infty , y \to \frac{0}{1 + 0} - 10$

$\Rightarrow y = - 10 \text{ is the asymptote}$
graph{((22)/(x+13))-10 [-40, 40, -20, 20]}