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Asymptote

# Asymptote - leading coeﬃcient of the denominator is the...

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Review the Asymptotes of f ( x ) = polynomial polynomial 1. Find VERTICAL asymptote : Check if f is in the LOWEST form (i.e., NO COMMON factors between the numerator and the denominator). Solve for x (i.e., the REAL zeros of the denominator) by setting the denominator = 0. The number of the vertical asymptotes = the number of REAL zeros of the denominator. 2. Find HORIZONTAL asymptote : Find the degree n of the numerator and the degree m of the denominator. If n < m y = 0 ( x -axis) is the ONLY ONE horizontal asymptote, n = m y = leading coeﬃcient of the numerator
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Unformatted text preview: leading coeﬃcient of the denominator is the ONLY ONE hori. asymp., n > m → NO horizontal asymptote. • The number of the horizontal asymptotes is either ONE (when n ≤ m ) or NONE (when n > m ). 3. Find OBLIQUE asymptote : • If n = m + 1, there is ONLY ONE oblique asymptote. Otherwise, there is NONE. • Use LONG DIVISION; the QUOTIENT is the oblique asymptote. • The number of the horizontal asymptotes is either ONE (when n = m + 1) or NONE (when n 6 = m + 1). 1...
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