Answer
See below.
Work Step by Step
a. Domain : The domain is the set of all $(x,y)$ in the xy plane.
b. Range: $R: 0 \lt z\leq 1$
c. Level Curves: The origin and the circles with center at (0,0) having radii $r \gt 0$
d. No boundary points
e. Both closed and open.
f. Unbounded