# How do you find the asymptotes for y = 5/(x - 1)?

Jan 28, 2016

The function will have a vertical and horizontal asymptotes.

#### Explanation:

This function has two asymptotes:

A vertical asymptote , corresponding to the vertical line passing through the $x$ value that makes the denominator equal to zero, i.e.:
when: $x - 1 = 0$
and:
$x = 1$
So the vertical line of equation $x = 1$ will be the vertical asymptote.

A horizontal asymptote that can be found observing the behaviour of the function when $x$ becomes very big (when $x$ tends to $\infty$).
As $x$ becomes big the function tends to become very small or tends to zero, i.e., $y \approx 0$.
The horizontal line of equation $y = 0$ will then be the horizontal asymptote (basically the $x$ axis!).

Graphically we can see them:
graph{5/(x-1) [-10, 10, -5, 5]}