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

Question

1529 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-12-14T21:10:57

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

Horizontal asymptote: $y= 1$

Oblique/Slant- None

$g(x) = (3x^2)/(x^2-9)$

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

$=> (x-3)(x+3)=0$

$=>x+3 = 0 => x= -3$

$=>x-3= 0 => x= 3$

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

$y= 1$

No oblique/slant asymptote

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