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MAC1105 Lecture Notes - Lecture 19: Asymptote

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16 Feb 2017

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Miami Dade College

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Mathematics: Calculus & Pre-Calculus

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5. 2 properties of rational functions notes: sterling. Provide a generalization to the terms listed in this section. Rational functions: functions that are in the form of r (x) = p(x) q(x) where you both p(x) and q(x) are polynomial functions while only q(x) can"t be a zero polynomial. Horizontal asymptote: a horizontal line that occurs when x is approaching either or , which would make f (x) approach l, can be written in one of two ways. F (x) l as x . Limx f (x) = l: helps describes a function"s end behavior, a function"s graph can intersect a horizontal asymptote. What if r (x) = p(x) q(x) = anxn++a0 bmxm++b0 was a rational function? q(x)"s degree is greater than p(x)"s degree m > n. Horizontal asymptote : y = 0 q(x)"s degree is one less than p(x)"s degree m = n 1. Rewritten : r (x) = mx + b + r (x)

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