Question

How do you find the Vertical, Horizontal, and Oblique Asymptote given `f(x) = 4/(x - 2)^3`?

Answer 1

The vertical asymptote is `x=2`
The horizontal asymptote is `y=0`
There are no oblique asymptote.

Explanation:

As we cannot divide by `0`, the vertical asymptote is `x=2`

There are no oblique asymptotes as the degree of the numerator is `<` degree of the denominator:

`lim_(x->-oo)f(x)=lim_(x->-oo)(4/x^3)=0^-`

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

The horizontal asymptote is `y=0`

graph{4/(x-2)^3 [-10, 10, -5, 5]}