How do you find all the asymptotes for function #y=1/(2x+4)#?

1 Answer
Jan 28, 2016

Answer:

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: #2x+4=0#
and:
#x=-4/2=-2#
So the vertical line of equation #x=-2# 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.

Graphically we can see them:
graph{1/(2x+4) [-10, 10, -5, 5]}