Sketching a graph (Limits) / that satisfies all these conditions? Help is appreciated. Help?

Question

Sketch the graph of an example of a function that satisfies all of the given conditions.

lim f=1 (as x approaches 0^-)
lim f =-1 (as x approaches 0^+)
lim f=0 (as x approaches 2^-)
lim f=1 (as x approaches 2^+)
f(2)=1, and f (0) is undefined

How would I draw this?
If someone could help, that would be AMAZING.
I'm up ALL night trying to do this one question.
Maybe a little drawing paint? IDK, but ANY HELP would be greatly appreciated!

Answer 1

Ok let's start with the last conditions:
f(2) = 1 (draw a closed point where x=2 and y=1)
f(0) is undefined (ok so we know there is nothing at x=0)

There are two places at which something interesting happens: one is at x=0 and the other is at x=2. Think of vertical lines at each of those points.

Now look at what is happening to the left and right of each of those lines. To the left of x=0, for example, the function is approaching 1. So you can draw anything (a line, a curve) where it looks like it will hit (0,1). Remember to use an open circle at (0,1) because f(0) is undefined.

Continue for the rest of the conditions.

Answer 2

The simplest example is the piecewise defined function at this link, scroll down, the definition is right below the graph:

http://s236.photobucket.com/albums/ff177/jsardi56/?action=view¤t=PieceDef9-27-07.jpg