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Easy: (ax + b)/(cx + d)
Factor first. A factor that cancels from the top and bottom makes a hole, not an asymptote. The zeros of the remaining denominator are the vertical asymptotes. For the horizontal asymptote compare degrees: a bottom-heavy function has y = 0; equal degrees give y = (leading coefficient on top) ÷ (leading coefficient on the bottom).
Find the vertical and horizontal asymptotes, and any hole.
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Both come from zeros of the denominator. If the factor cancels with the numerator, the graph has a hole there; if it doesn't, the graph has a vertical asymptote.
If the bottom's degree is higher, y = 0. If the degrees are equal, y = the ratio of the leading coefficients. If the top's degree is higher, there is no horizontal asymptote.
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