Graphical Behavior

Rule 3

If the degree of the numerator is larger than the degree of the denominator, then there is no horizontal asymptote.

Example. Determine the horizontal asymptote of the function.

Since the numerator is second degree (quadratic) and the denominator is first degree (linear), the degree of the numerator is larger than the degree of the denominator. Therefore, the function has no horizontal asymptotes.