Question

What are the asymptote(s) of `f(x) = (3x) / (x+4)`?

Answer 1

`f(x)` has horizontal asymptote `y=3` and vertical asymptote `x=-4`

Explanation:

When `x=-4` the denominator of `f(x)` is zero and the numerator is non-zero. So this rational function has a vertical asymptote `x=-4`.

`(3x)/(x+4) = 3/(1+4/x) -> 3` as `x->oo`

So `f(x)` has a horizontal asymptote `y = 3`

graph{(3x - xy - 4y)(x+4+y0.001)(y-3-x0.001) = 0 [-25.25, 14.75, -7.2, 12.8]}