When There Is No Horizontal Asymptote?

To find horizontal asymptotes: If the degree (the largest exponent) of the denominator is bigger than the degree of the numerator, the horizontal asymptote is the x-axis (y = 0). If the degree of the numerator is bigger than the denominator, there is no horizontal asymptote.

How do you know if a function has no horizontal asymptote?

If the polynomial in the numerator is a lower degree than the denominator, the x-axis (y = 0) is the horizontal asymptote. If the polynomial in the numerator is a higher degree than the denominator, there is no horizontal asymptote.

Can a horizontal asymptote not exist?

determining the limit at infinity or negative infinity is the same as finding the location of the horizontal asymptote. there's no horizontal asymptote and the limit of the function as x approaches infinity (or negative infinity) does not exist.