There are three rules of finding the horizontal asymptote depending on the orders of the numerator and denominator. If the degrees are equal for the numerator and the denominator, then the horizontal asymptote is equal to y = the ratio of the coefficients of the highest order from the numerator and the denominator. If the degree in the numerator is less than the degree in the denominator, then there the x axis is the horizontal asymptote. If on the other hand, the order in the numerator is greater than that of the denominator, then there is no horizontal asymptote.
