How do you find the asymptotes for g(x) =( 3x^2)/(x^2 - 9)g(x)=3x2x2−9?

1 Answer
Vikki
Dec 14, 2015

Vertical asymptote: x= -3, x= 3x=−3,x=3

Horizontal asymptote: y= 1y=1

Oblique/Slant- None

Explanation:

g(x) = (3x^2)/(x^2-9)g(x)=3x2x2−9

Vertical asymptote- set the denominator to zero
x^2 - 9 =0x2−9=0

=> (x-3)(x+3)=0 ⇒(x−3)(x+3)=0

=>x+3 = 0 => x= -3⇒x+3=0⇒x=−3

=>x-3= 0 => x= 3⇒x−3=0⇒x=3

Horizontal asymptote- Degree of numerator and denominator are the SAME- then horizontal asymptote is

y= 1y=1

No oblique/slant asymptote

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