How do you find the asymptotes for #(2x-4)/(x^2-4)#?
1 Answer
Dec 16, 2015
H.A. @
V.A. @
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
The rule for vertical asymptotes:
- There is a vertical asymptote at any value that will cause the function to be undefined.
Because
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.