Question

a

Answer 1

Your domain/range sets aren't right... What happens when you plug in \((x,y)=(1,1)\) ?

Answer 2

I think Wolfram plots keep the "zero elsewhere" portion of the plots because it doesn't like displaying surfaces that stop abruptly. You can ignore the flat portions of the graphs.

Answer 3

I am! Your domain is correct, but the range has a slight mistake. Your answer only considers the top hemisphere (the positive half). Changing to \(|z|\le1\) fixes the issue.

Answer 4

and you're welcome!

Answer 5

Yes, correct.