Answer
See below.
Work Step by Step
a. Domain : The domain is the set of all $(x,y)$ in the xy -plane.
b. Range: A set of all Real numbers
c. Level Curves: We have for $f(x,y)=0 \rightarrow$ $y \pm x$ and for $f(x,y)=c\ne 0$ hyperbolas with center (0,0) and foci on the x-axis when $c\gt 0$ and on the y-axis when $c\lt0$
d. No boundary points
e. Both closed and open.
f. Unbounded
