# How do you find the horizontal asymptote for y = x / (x-3)?

Jul 11, 2018

$\text{horizontal asymptote at } y = 1$

#### Explanation:

$\text{Horizontal asymptotes occur as}$

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

$\text{divide terms on numerator/denominator by } x$

$y = \frac{\frac{x}{x}}{\frac{x}{x} - \frac{3}{x}} = \frac{1}{1 - \frac{3}{x}}$

$\text{As } x \to \pm \infty , y \to \frac{1}{1 - 0}$

$y = 1 \text{ is the asymptote}$
graph{x/(x-3) [-10, 10, -5, 5]}