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Rational functions: asymptotes and holes
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Learn it For y = p(x)/q(x) in lowest terms: vertical asymptotes where q(x) = 0. If a factor cancels, there is a hole instead. Horizontal asymptote: compare degrees (top lower → y = 0; equal → ratio of leading coefficients; top higher → none).
Example: y = (2x + 1)/(x − 3).
- Vertical asymptote: x = 3.
- Equal degrees: horizontal asymptote y = 2/1 = 2.
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