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

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Answer 1 · 2016-11-10T12:58:36

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

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]}

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