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Polynomials

YOUR TURN:

Draw a rough sketch of

f( x ) = -x^6 + some x stuff

and make a note of its features.
 


Let's move on to odd degree polynomials.  Our easiest odd degree guy is the disco graph...  We really should give him a more mathematical name.  How about Standard Cubic Guy?

f( x ) = x^3Standard Cubic GuyNotice those tails.  They go in opposite directions!

Boring without any wobbles though.

Pop this guy into a graphing calculator:

f( x ) = x^3 - 4x


The tails do the same thing as Standard Cubic Guy...  But, we get to cross three times (3rd degree!)		roller coaster graph with one valley and one mountain

 

So, what would this guy look like?

f( x ) = -x^3 + some x stuff ... the - flips it up-side-down ... the some x stuff puts some potential wobbles inroller coaster graph with one valley and one mountain