What does f( x ) = x^5 look like?  No wobbles, that's for sure.
Put it in a graphing calculator...

Standard Cubic Guy
Just like f( x ) = x^4
looked like f( x ) = x^2 ,
this guy looks like f( x ) = x^3 ,
but his shoulders are wider.

What would he look like with wobbles?

f( x ) = x^5 + some x stuff

His left tail starts low like the disco graph.  He can cross the x-axis, at most, five times...

Tails go in opposite directions...

May have two mountains and two valleys.

roller coaster graph with two valleys and two mountains



Draw a rough sketch and make a note of its features.

f( x ) = -x^5 + some x stuff

f( x ) = x^7 + some x stuff