Order+of+Transformations

The order of operations for the transformation of a function can be performed from left to right, as if the function was an english word.

For the transformation f(x) = a f(b(x+c)) + d, the order of operations is:

1. vertical stretch/compression by a factor of a 2. horizontal stretch/compression by a factor of b 3. horizontal translation c units left/right 4. vertical translation d units up/down

I was playing around with some numbers and I selected a parabola y= (x+2)^2 + 7 to be the original function. I subsequently subjected that function to the transformation f(x) = -1/3 f[-1/5(x+3)] + 7. ALL THE GOODIES.

If the "left to right" method was correct, the vertex of the original parabola would shift from (-2,7) to (7, 14/3)



The vertex of the new transformed parabola was indeed (7,14/3).

In conclusion, the transformation of a function can be treated as if one were reading the function as a word. Transformations are preformed from left to right (a first, then b, then c, then d).

P.S. Please realize either the horizontal stretch/compression or the vertical stretch/compression can be done first or second and that either the horizontal translation or the vertical translation done third or fourth respectively. The 'left to right' method is simply a convenient pneumonic should you choose to use it.