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Easy: Equal degrees
As x → ∞, only the highest powers matter. If the bottom has the higher degree, the limit is 0. If the degrees are equal, the limit is the ratio of the leading coefficients. If the top has the higher degree, the function grows without bound: the limit is ∞ or −∞, depending on the signs.
Evaluate each limit, or write ∞ or −∞.
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As x gets huge, the highest-power terms grow much faster than the rest, which become negligible in comparison.
If the limit as x → ∞ or x → −∞ is a number L, the line y = L is a horizontal asymptote of the graph.
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