So, what would this look like?

f ( x ) = -x^4 + some x stuff ... the ( - ) flips it up-side-down

Some basic shape

Both tails point down!

f ( x ) = -x^4 + some x stuff

Here are a couple of questions for you:

(Think about them carefully before reading on!)


Can you draw a parabola that crosses the x-axis more than 2 times?

2Since the basic shape of  f ( x ) = x^4 + some x stuff


rough shape of f ( x ) = x^4, can he ever cross the x-axis more than 4 times?

The answer to 




is a pretty obvious "no" -- because of the

parabola shape







... to make him cross more than 4 times, you'd have to bend

one of his tails down...  But, you aren't allowed to break his basic shape.  (You'll understand this more when you read the next section.) So, the answer is "no."