Rational Functions

Features of f(x) = P(x)/Q(x), degree of P is n, degree of Q is m

Hole

x = c where (x - c) divides both P and Q

Vertical asymptote

x = c where the simplified Q (c) = 0

Horizontal asymptote, n < m

y = 0

Horizontal asymptote, n = m

y = \frac{a_{n}}{b_{m}}

ratio of leading coefficients

Slant asymptote, n = m + 1

y = quotient of P (x) \div Q (x)

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