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Graphing Polynomials
Graphing polynomials can be easy if you know what all the xintercepts 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 lessmanageable.
Using Function Shift Rules to Plot Even Powers
You can easily plot even powers of x if they are in a functionshift 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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Using Function Shift Rules to Plot Odd Powers
You can easily plot odd powers of x if they are in a functionshift 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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 Fall '09
 Crandall
 Anthropology, Leftwing politics

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