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

1 Answer
Nov 10, 2016

Answer:

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]}