Visualising a graph from $\mathbb{R^3}$ to $\mathbb{R}$

Question

Given a function, any function, exempli gratia, $$f(x,y,z)=\frac{x^2y}{z}$$

It's range will be whole of $\mathbb{R}$(???). Plotting the graph does not make sense. How can I, if I can, visualise this graph so I can study behaviour of the function?

Answer 1

Via Maple 16, and the following codes, you can easily plot the contor plots of the function not the function and study the graph better:

>f:=(x,y,z)->x^2*y/z:

>for i from 1 t0 5 do plot3d(f(x,y,i),x=-10..10,y=-10..10) od;