End Behavior of the Graph of a Polynomial

```End Behavior of the Graph of a Polynomial
End Behavior β what happens when π gets very large, approaching ββ and approaching +β?
π(π) = ππ ππ + ππβπ ππβπ + β― + ππ π + ππ
ο· This is a POLYNOMIAL. Its degree is π and its leading coefficient is ππ .
ο· The degree and the leading coefficient tell you about the End Behavior of its graph:
If the degree is ODD
coefficient is positive
coefficient is negative
If the degree is EVEN
coefficient is positive
coefficient is negative
It behaves like π¦ = π₯ 3
It behaves like π¦ = π₯ 2
lim π(π₯) = ββ
π₯βββ
lim π(π₯) = β
π₯β+β
Itβs like π¦ = βπ₯ 3
lim π(π₯) = β
π₯βββ
lim π(π₯) = ββ
π₯β+β
lim π(π₯) = β
π₯βββ
lim π(π₯) = β
π₯β+β
Itβs like π¦ = βπ₯ 2
lim π(π₯) = ββ
π₯βββ
lim π(π₯) = ββ
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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