You've got me GoldenLeaf
I am sure other mathematicians would like to comment on this one.
I think
It is a function because every real x value has no mot than 1 y value
EDIT: Chris is correct this IS an even function.
The domain is $$\{x:x\in R\}$$
The range is y=o, y=1 I am not sure how to display this properly.
This is a non-continuous graph . I would describe it as a step graph.
I'd be interested to hear how your teacher answers these. 