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

1 Answer
Gió
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 #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]}

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