We can tell if a graph has a horizontal asymptote by comparing the degrees of the numerator and the denominator. If the bottom has the bigger degree, the asymptote is y=0. If they're both the same degree, the asymptote is the ratio of the coefficients. If the degree is bigger on top, there is no horizontal asymptote. Remember that graphs can only sometimes cross through a horizontal asymptote but only through the middle of the graph.
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