End Behavior of the Graph of a Polynomial End Behavior β what happens when π gets very large, approaching ββ and approaching +β? π(π) = ππ ππ + ππβπ ππβπ + β― + ππ π + ππ ο· This is a POLYNOMIAL. Its degree is π and its leading coefficient is ππ . ο· The degree and the leading coefficient tell you about the End Behavior of its graph: If the degree is ODD and the leading and the leading coefficient is positive coefficient is negative If the degree is EVEN and the leading and the leading coefficient is positive coefficient is negative It behaves like π¦ = π₯ 3 It behaves like π¦ = π₯ 2 lim π(π₯) = ββ π₯βββ lim π(π₯) = β π₯β+β Itβs like π¦ = βπ₯ 3 lim π(π₯) = β π₯βββ lim π(π₯) = ββ π₯β+β lim π(π₯) = β π₯βββ lim π(π₯) = β π₯β+β Itβs like π¦ = βπ₯ 2 lim π(π₯) = ββ π₯βββ lim π(π₯) = ββ π₯β+β NOTE: This only applies to the End Behavior. What happens in the middle depends on the rest of the polynomial. M1111 QuickNotes/PolynomialEndBehavior.docx 6/23/2016 5:41 PM D.R.S.

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