This applet will help you in visualizing the effects of transformations on functions. Move the sliders on the right to change the translation and scaling factors ...

What if instead of defining a mesh as a series of vertices and edges in a 3D space, you could describe it as a single function ... scaling, and transformations modify the sample point before ...

But “there are probably fewer areas of math where they don’t have applications ... the same value — meaning that there are infinitely many transformations that can leave the function unchanged.