Equation of a horizontal and vertical asymptote

Apr 2008
80
2


Consider the rational function f(x)= 3x^2 - 12 / x^2 - 3x + 2
A. Give the equation of the horizontal asymptote.

B. Give the equation(s) of any vertical asymptotes.
Thanks
 
Apr 2008
80
2
Is this right?
f(x)= (3x^2 - 12) / (x^2 - 3x + 2)

horizontal asymptote: y = 3

Vertical Asymptote: (x^2 - 3x + 2) = 0

(x - 2)(x - 1) = 0
x = 2
x = 1

Vertical Asymptotes: x = 1, x = 2
 
Sep 2009
32
4
Milwaukee, Wisconsin
Is this right?
f(x)= (3x^2 - 12) / (x^2 - 3x + 2)

horizontal asymptote: y = 3

Vertical Asymptote: (x^2 - 3x + 2) = 0

(x - 2)(x - 1) = 0
x = 2
x = 1

Vertical Asymptotes: x = 1, x = 2
Not quite, simplify the numerator too. Something will cancel out and you will have one less vertical asymptote. But you have the general idea behind this.