How do you identify all asymptotes or holes for f(x)=(2x)/(x^2-1)f(x)=2xx2−1?

1 Answer
Nickel
Sep 26, 2016

VA: 1,-1
HA: 0
SA: N/A

Explanation:

Vertical asymptote: Set denominator = 0 but factor first
x^2-1x2−1=(x-1)(x+1)(x−1)(x+1)
(0-1)=-1(0−1)=−1
(0+1)=1(0+1)=1

11 and -1−1 are your vertical asymptotes

Horizontal asymptote: When the x with the biggest power in the numerator is less than the x with the biggest power in the numerator, the horizontal asymptote is 00.

Since a horizontal asymptote exists, then a slanted asymptote does not exist. It would only exist if the x with the biggest power in the numerator is biggest than the x with the biggest power in the denominator.

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