Presentation on theme: "WARM UP Zeros: Domain: Range: Relative Maximum: Relative Minimum:"— Presentation transcript:
1 WARM UPZeros:Domain:Range:Relative Maximum:Relative Minimum:Intervals of Increase:Intervals of Decrease:
2 SymmetryEssential Question: How do you determine the shape and symmetry of the graph by the polynomial equation?
3 Even, Odd, or Neither Functions Not to be confused with End behaviorTo determine End Behavior, we check to see if the leading degree is even or oddWith Functions, we are determining symmetry (if the entire function is even, odd, or neither)
4 Even and Odd Functions (algebraically) A function is even if f(-x) = f(x)If you plug in x and -x and get the same solution, then it’s even.Also: It is symmetrical over the y-axis.The easiest thing to do is to plug in 1 and -1 (or 2 and -2)if you get the same y, then it’s Even.If you get the opposite y, then it’s Odd.If you get different y’s, then it’s Neither.A function is odd if f(-x) = -f(x)If you plug in x and -x and get opposite solutions, then it’s odd.Also: It is symmetrical over the origin
5 Y – Axis Symmetry Fold the y-axis Even Function(x, y) (-x, y)-51-42-134411-1-4-2-3(x, y) (-x, y)
6 Test for an Even Function A function y = f(x) is even if , for each x in the domain of f.f(-x) = f(x)Symmetry with respect to the y-axis
7 Symmetry with respect to the origin (x, y) (-x, -y)(2, 2) (-2, -2)(1, -2) (-1, 2)Odd Function
8 Test for an Odd Function A function y = f(x) is odd if , for each x in the domain of f.f(-x) = -f(x)Symmetry with respect to the Origin
9 Ex. 1Even, Odd or Neither?GraphicallyAlgebraicallyEVEN
10 Ex. 2Even, Odd or Neither?GraphicallyAlgebraicallyODD
11 Ex. 3Even, Odd or Neither?GraphicallyAlgebraicallyEVEN
12 Ex. 4Even, Odd or Neither?GraphicallyAlgebraicallyNeither
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