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

Dec 16, 2015

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.