This demonstration graphs a function f[r,t] over a rectangular domain. By default, the domain is set to 0 ≤ r ≤ 1, 0 ≤ t ≤ 2π and the function is set to f[r,t] = r²cos(2t).

In the window labeled "Domain and Range", you can choose both the center and radius of a red disc domain in the xy-plane 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) over the red disc domain.

In the "Graph: f(x,y)" window, when the "Range" checkbox is selected will display the range of the function over the red disc domain.  This range will be displayed along the z-axis.  When the "ShowGraph" checkbox is selected this window will display the function graph over the domain defined by r and t in the control window, as well as the function graph of the red disc domain.