Answer
See below.
Work Step by Step
a. Domain : The domain is set of all $(x,y)$ in the xy plane
b. Range: $R: z\geq 0$
c. Level Curves: We have for $f(x,y)=0$: origin and for $f(x,y)=c$: ellipses with center (0,0) and major and minor axes along $x$ and $y$-axes.
d. No Boundary points
e. Both Closed and open.
f. Unbounded