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

Question

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

Answer 1

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.