# How do you find the asymptotes for #g(x) = (4x^2+11) /( x^2+8x−9)#?

##### 1 Answer

Jan 16, 2016

H.A. @

V.A.s @

No S.A.

#### Explanation:

Original Equation:

Factor:

**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 degrees in this equation are the same, 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 slant 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 degrees are the same, there is no slant asymptote.