We know whether or not a graph has a horizontal asymptote by looking at the degree of the numerator and denominator and we can compare the degree on the bottom and the top to find out if the degree is a horizontal asymtote. Now your options that you have to find if the graph is a horizontal asymptote, your first option is to see if you get a bigger degree on the bottom that way you can ensure the asymptote is y=0. Your second option is to see if the degree is the same, that way the asymptote is the ratio of the coefficient. The last option is to see if the bigger degree on top has no horizontal asymptote because only the middle can have an asymptote.
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