Question

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

Answer 1

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 `oo`).
As `x` becomes big the function tends to become very small or tends to zero, i.e., `y~~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]}