How do you find the asymptotes for #(2x-4)/(x^2-4)#?

1 Answer
Dec 16, 2015

Answer:

H.A. @ #x=2#
V.A. @ #x=2# and #x=-2#
No S.A.

Explanation:

The rules for horizontal asymptotes:

  • When the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote.
  • When the degree of the numerator is the same as the degree of the denominator, there is a horizontal asymptote at #x=0#
  • When the degree of the numerator is less that the degree of the
    denominator, there is a horizontal asymptote at the quotient of the leading coefficients.

Because the denominator is bigger, there is a horizontal asymptote at #x=2#

The rule for vertical asymptotes:

  • There is a vertical asymptote at any value that will cause the function to be undefined.

Because #2# and #-2# will cause the equation to be undefined (the denominator is equal to #0#), there is a vertical asymptote at #x=2# and #x=-2#

The rule for vertical asymptotes:

  • When the degree of the numerator is exactly #1# more than the degree of the denominator, there is a slant asymptote at the quotient of the numerator and the denominator. (You have to divide the top by the bottom)

Because the denominator is greater, there is no slant asymptote.