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**7.2 Polynomial Functions and Their Graphs**

Andrew Fisher 8-2

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**Local Minimum and Maximum**

Local minimum and maximum are the highest and lowest points in their “neighborhood” on the graph. 2 points on either side of the minimum or maximum f(x1) and f(x2) are less than or greater than f(a).

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Example Find the Local Minimum and Maximum .

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Answers Local Minimum (-3,6) Local Maximum (3,-6)

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**Increasing and Decreasing Functions**

F is increasing over an open interval if for every x1<x2 in the interval, f(x1)<f(x2) F is decreasing over an open interval if for every x1<x2 in the interval, f(x1)>f(x2)

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End Behavior F(x)=ax^n a>0 a<0 Left Right Left Right N is even Rise Rise Fall Fall N is odd Fall Rise Rise Fall

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Find the End Behavior x^ x^2 X^ x^5 2x^ x^3

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**Answers Rise on left 4. Fall on left Rise on right Fall on right**

2. Fall on left Falls on left Rise on right Rise on right 3.Rise on left Rise on left

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