Answer
The vertical asymptotes are x=-1 and x=1.
The only horizontal asymptote is y=0.
There are no oblique asymptotes.
Work Step by Step
To find asymptotes, first, we must make sure the function is in the lowest terms.
To find vertical asymptotes, we must find the values that make the denominator equal zero. In this case:
$x^4-1=0$
$x^4=1$
$\sqrt[4]{x^4}=\sqrt[4]1$
$x=\pm1$
There are two cases to determine horizontal asymptotes. If the degree of the denominator is greater than the degree of the numerator, the horizontal asymptote will be y = 0. If the degrees of both the numerator and denominator are the same, the horizontal asymptote is the ratio of the leading coefficients.
In this case, we can see that the degree in the denominator is greater than the one in the numerator, so the horizontal asymptote is y=0.
To determine oblique asymptotes, the degree of the numerator must be one degree greater than the degree of the denominator. Since that requirement is not being met here, there are no oblique asymptotes.