This demonstration shows the three-dimensional domain and the (one-dimensional) range of a function f(x,y,z). By default, the domain is set to -1 ≤ x ≤ 1, -1 ≤ y ≤ 1, -1 ≤ z ≤ 1 and the function is set to f(x,y) = x2 - y2 + z2.
In the window labeled Domain and Range, you can choose both the center and radius of a red spherical domain using the white and red hotspots, respectively. The magenta line segment along the z-axis in this window shows the range of f(x,y,z) of this red domain.