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Our easiest odd degree guy is the disco graph.  We really do need to give him a more mathematical name...  Standard Cubic Guy!

f ( x ) = x^3

graph of f ( x ) = x^3


Notice that these tails point in the opposite direction (unlike the even degree guys). 

Eh...  it's boring without those wobbles...

Check this guy out on the graphing calculator:

f ( x ) = x^3 - 4x

You should get:

The tails do the same thing as Standard Cubic Guy...

But, this guy crosses the x-axis
3 times...  and the degree is?

3!

graph of f ( x ) = x^3 - 4x

Can this guy ever cross 4 times?  Nope!  Not unless you bend one of his tails...  But, then he'd be an x^4 guy!

03-graphing-polynomials-06.gif