# How do you find the asymptotes for y = 6/x?

Jan 26, 2016

Vertical asymptote at $x = 0$
Horizontal asymptote at $y = 0$

#### Explanation:

Given
$\textcolor{w h i t e}{\text{XXX}} y = \frac{6}{x}$
This relation ship is defined for all values of $x$ except $x = 0$;
$x$ may approach $0$ as closely as we like, but it can never be $= 0$;
therefore $x = 0$ is an asymptote.

As $x \rightarrow \infty$
$\textcolor{w h i t e}{\text{XXX}} y \rightarrow 0$
but $y$ is never $= 0$;
therefore $y = 0$ is an asymptote.
graph{y=6/x [-28.86, 28.85, -14.43, 14.43]}