Question

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

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: `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]}