Algebra 2 Graphing Higher Degree Equations
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Big Exponents
Graphing Higher Degree Equations

 

 What's the graph of Y = X 4 look like?

 Well pretty much like the graph of Y = X 2 but narrower.

 

 The graph of Y = X 4 is narrower than the graph of Y = X 2
 everywhere except between X = -1 and X = 1.
 In that area, the graph of Y = X 4 is wider.
 
 This is because when you multiply a fraction times itself
 the answer is smaller than the fraction you used.
 

 

 
 And the more times you multiply the fraction times itself
 the smaller the answer gets ...
 

 

 
 And a funny thing happens when you put ANY exponent on 1 ...
1-5  = 1
1-1  = 1
10  = 1
13  = 1
12000  = 1
1(any exponent)  = 1
 
 So what does that mean to us?
 It means that if we have an equation like:
 

 Y = X(any exponent)

 When X = 1 , then Y = 1 too!

 

 
 OK, back to the big exponents.
 What does the graph of Y = X 5 look like?
 Pretty much like the graph of Y = X 3 but narrower.
 Except ... wait for it ...
 
 in the area between X = -1 and X = 1.

 

 
 So the deal is ...

 Y = X(even number)

 
 All of these equations with even number exponents
 have the same "U" shape as Y = X 2.
 The bigger the exponent, the narrower the "U"
 except between X = -1 and X = 1.
 
 AND ...

 Y = X(odd number)

 
 All of these equations with odd number exponents
 have the same shape as Y = X 3.
 The bigger the exponent, the narrower the "U"
 except between X = -1 and X = 1.
 

   copyright 2005 Bruce Kirkpatrick

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