I haven't shown any of the equations involved. My idea here was simply to show what the different transformations are: for example, a horizontal shear may look like a rotation, but it isn't.[br][br]I wonder if the absence of equations will encourage you to look for patterns?[br][br]Can you find any of the equations yourself?[br][br]Geometry people: can you find the focus and directrix of any of the transformed curves?[br][br]Calculus people and sneaky algebra people: can you find tangent lines?[br][br]Linear algebra people: can you quickly rule out some of these as linear transformations, and find matrices that describe the others? What are the eigenvectors and eigenvalues?