Answer
Domain: $x: (-\infty,\infty); y: (-\infty,\infty); z: (-\infty,\infty);$
Range: $f(x,y,z): (-\infty,\infty);$
Level surface: $f(x,y,z)=c$ (constant)
Work Step by Step
Function: $f(x,y,z)=x^{2}+y^{2}-z$
Domain: x, y, z can be any real numbers and (x,y,z) can be any point in the X-Y-Z system.
Range: $f(x,y,z)$ can be any real number.
Level surface: $f(x,y,z)=c$ (constant)
$x^{2}+y^{2}-z=c$
$z=x^{2}+y^{2}-c$ represent a series of paraboloids.
For example, when $c=-1$,
$z=x^{2}+y^{2}+1$ can be plotted as shown in the figure.
