Find the vertical, horizontal, and oblique asymptotes, if any, of the given rati

Question

Find the vertical, horizontal, and oblique asymptotes, if any, of the given rational function x-27 x2+x-12 R(x) = Find the vertical asymptote(s), if any, of the function. Select the correct choice below and fill in any answer boxes within your choice O A. The vertical asymptote(s) is/are x= O B. There is no vertical asymptote. Find the horizontal asymptote(s), if any, of the function. Select the correct choice below and fill in any answer boxes within your choice. (Simplify your answer. Use a comma to separate answers as needed.) The horizontal asymptote(s) is/are y= 1. (Simplify your answer. Use a comma to separate answers as needed.) A. B. There is no horizontal asymptote.

Explanation / Answer

R(x) = ( x^3 - 27 ) / ( x^2 + x - 12 )

factoring the denominator

x^2 + x - 12 = 0

( x +4) ( x-3 ) = 0

x = - 4 , x = 3

vertical asymptotes are x = - 4 , x = 3

b) dividing the rational function

we get y = x -1

which is oblique asymptote

so, there are no horizontal asymptotes

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