I am returning to school after a long break. One of my assignments is a mix of ODE and discrete math and is clogging my mind.

I have been struggling on my 12 question homework for 4 hours now and have made it 1/4 of the way through. Luckily i have found this forum and hope someone(s) can help.

The question is this:

Find a continuous function:

f : [0, 1] --> [0, 1] with exactly three fixed points and draw its graph.

The fixed points is throwing me for a loop.(Headbang)

Any suggestions??