Transformation is warping rubber sheet with shit on it, twisting
   and bending, squishing and stretching it. The shit on it warps
   too and looks weird when we try to use the same coordinate
   system at the same time that we SHOULD BE using an overlaying
   coordinate system. Oh and the shit on it can TELEPORT too.

   In short, warping spacetime in a relative dimension. But I'm a
   spacetime nut tongue emoticon I hate all the names tho'. I'd
   teach transformations using a graphics program and students
   would have to make crap show up on the screen using the right
   commands. The right commands would ALSO happen to be the names
   for the four categories of transformations

   Something like that.

   I wouldn't use this type of stuff
   [1]http://www.purplemath.com/modules/fcntrans2.htm but whatever.
   They're obsessed with the damn curvy lines. OO - we can move it
   over two spaces in a difficult way... thanks Newton but we have
   video games now and we work in pixels now. Thanks for the
   concepts; we'll take over from here: I need to move Mario across
   the screen and make a realistic looking JUMP utilizing the
   conditions of the Level he's on.

   He jumps differently in water than in air so a single jump
   results in a different distance.... and ooh we're going to give
   him teleport so the same jump shows up somewhere else.

   I'm being purposely unhelpful. I have to get my rant out. I'd be
   failed by my Trig teacher. My Trig teacher was very annoyed with
   how I thought about things 'til I explained myself. In my mind,
   I translated all mathematical concepts into BASIC 'cause that's
   what my Tandy Color Computer 2 had, and I imagined I was making
   a little video game. This is back in 1988/89 and of those
   Newtonian concepts were perfectly embedded in making things show
   up on the screen.

References

   Visible links
   1. http://www.purplemath.com/modules/fcntrans2.htm