Find all the asymptotes of the rational function fx x3 x2

Find all the asymptotes of the rational function f(x) = x^3 + x^2 - x - 4/x^2 - 1 To get the graph of y = - f(x), you reflect y = f(x) across the __

Solution

f(x) = ( x^3 - x^2 -x -4)/(x^2 -1)

Vertical asymtote : x^2 - 1 =0

(x +1)(x-1) =0

x = -1 ; x = 1

Horizontal Asymtote : If the degree of numerator is greater than denominator then there is no horizontal asymtote. We check for slant asymtote:

( x^3 - x^2 -x -4)/(x^2 -1) = x -1     - 5/(x^2 -1)

Slant Asymtote : y = x-1