I don't know where the tradition comes from to represent functions R^2->R in 3D, but it certainly isn't a great idea. Folding a 3D picture onto a computer screen always hides function features. For example, in all functions given here, symmetries aren't recognizable. Why not use contourf plots?
Second, the jet/rainbow colormap is deceiving. A better choice is visually uniform colormap such as gray, paluris (MATLAB), or viridis (mpl).