Question

How do you find the vertical, horizontal or slant asymptotes for `y = 3/(x + 4)`?

Answer 1

Vertical asymptote is `x=-4`
Horizontal asymptote is `y=0`

Explanation:

The equation is undefined at `x=-4` as `1/(x-4)->1/0` and division by 0 'is not allowed'. So excluded value is `x=-4`

This `x=-4` is a vertical asymptote.
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

As the magnitude of `x` increases in both the positive and negative directions then `|x+4|` becomes so large that `3/(x+4)` becomes exceptionally small.

Thus

`lim_(x->-4) 3/(x+4) = +-0`