Set theory with functions

Hello there,

I have the following assignment that my teacher gave me:

Let and the function be .

Give a directed graph of .

Okay I've drawn that one, it looks like this: see below

Give a directed graph of .

I've that one too: see below

Give a directed graph of

How should I draw this one??? Is it like drawing one with the following relation set: ?

now the next question is whether this a function is. I have no idea, I guess it can be a function. But I need to argument that, which I can't... can somebody help me out with this?

If I've made some mistakes up there, can somebody please correct me?

Thanks! If you have any tips or any notation style that I can adapt, please give me a suggestion ^^!

Thanks for everything and your time,

Umbrella

PS: somehow my curly braclets don't work in Latex, how can I fix that :(?

My image: http://img163.imageshack.us/img163/1818/imag0039yn.jpg