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find the vertical, horizonal, and oblique asymptotes, if any , for the following rational function.

Find the vertical, horizontal, and oblique asymtotes, if any , for the following rational function.  T(x)=x^3/x^4-81 ?
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1 Answer

Vertical asymptotes:
Where denominator = 0.
x4 - 81 = (x2+9)(x2-9) = (x2+9)(x+3)(x-3)
Since x = 3 or x = -3, would make the denominator 0, those are vertical asymptotes.
Since the degree of the denominator is greater than the degree of the numerator, the 
horizontal asymptote is y = 0, and there are no oblique/slant asymptotes.