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

Vertical asymptote:

Horizontal asymptote:

Oblique/Slant- None

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

No oblique/slant asymptote

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To find the asymptotes of the function ( g(x) = \frac{3x^2}{x^2 - 9} ), we first identify any vertical asymptotes by determining where the denominator equals zero. Here, the denominator ( x^2 - 9 ) equals zero when ( x = 3 ) or ( x = -3 ).

So, the vertical asymptotes are ( x = 3 ) and ( x = -3 ).

Next, we check for horizontal asymptotes. If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is at ( y = 0 ). If the degrees are equal, the horizontal asymptote is the ratio of the leading coefficients. If the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote.

In this case, both the numerator and denominator have the same degree (2), so the horizontal asymptote is the ratio of their leading coefficients, which is ( 3/1 = 3 ).

Therefore, the horizontal asymptote is ( y = 3 ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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