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

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;