Horizontal and vertical asymptotes help!?

Question

Ok I need to find the horizontal and vertical asymptotes of the following equation, and I have no idea how! Please help me lol

(3x)/(x^2+2)

Any help is greatly appreciated!

Answer 1

Vertical asymptotes occur when the denominator equals zero.

x^2 + 2 = 0

x^2 = -2

no real answer, so no vertical asymptote

Horizontal asymptotes depend on the power of the numerator and denominator.

If the power on top is higher, there is no horizontal asymptote.

If the power on the bottom is higher, the horizontal asymptote is at 0 (y = 0).

If the two powers are equal (same top and bottom), the horizontal asymptote is the ratio of the leading coefficients.

In this problem, the power on top is 1 (highest exponent) and on bottom is 2 (highest exponent). The power on the bottom is bigger (2>1), so the horizontal asymptote is y = 0.

Hope that helps!