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Graphing-Polynomials

# Graphing-Polynomials - Graphing Polynomials Graphing...

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From MathMotivation.com – Permission Granted For Use and Modification For Non-Profit Purposes Graphing Polynomials Graphing polynomials can be easy if you know what all the x-intercepts are. Or graphing polynomials, by hand without a graphing calculator, can be only accomplished using calculus. We will look at methods of graphing more “manageable” polynomials as well as some methods of quickly predicting behavior of the less-manageable. Using Function Shift Rules to Plot Even Powers You can easily plot even powers of x if they are in a function-shift form since all even powers of x like y=x 2 , y=x 4 , y=x 6 , y=x 8 , etc have a similar “U” shape containing points (0,0), (1,1), and (-1,1), as shown below. The higher the power on x, the more “flattened” out the curve will be between x=1 and x=-1 and the steeper the curve will be for x>1 and x<-1. Example: Graph y = (x –3) 10 + 1 by using function shift rules. This will be a shift of y=x 10 right 3 and up 1. So, we get a flattened out “U” shaped curve with the points (0,0), (1,1), and (-1,1) shifted right 3 and up 1 as shown below.

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From MathMotivation.com – Permission Granted For Use and Modification For Non-Profit Purposes Using Function Shift Rules to Plot Odd Powers You can easily plot odd powers of x if they are in a function-shift form since all even powers of x like y=x 3 , y=x 5 , y=x 7 , y=x 9 , etc have a similar “S” shape containing points (0,0), (1,1), and (-1,-1), as shown below. The higher the power on x, the more “flattened” out the curve will be between x=1 and x=-1 and the steeper the curve will be for x>1 and x<-1, as was the case with the even powers. Example: Graph y = (x + 2) 11 - 1 by using function shift rules. This will be a shift of y=x 11 left 2 and down 1. So, we get a flattened out “S” shaped curve with the points (0,0), (1,1), and (-1,-1) shifted left 2 and down 1 as shown below.
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Graphing-Polynomials - Graphing Polynomials Graphing...

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