Functions Transformations/Translations/Dilations/Reflections/Rotations
The Basics
What is a Translation? A translation moves the graph up, down, and side to side.
What is a Dilation? A dilation makes the function skinnier or larger.
What is a Reflection? A reflection is a mirror image. This flips the function over the x or y axes.
What is a Rotation? It depends on the type of line but a rotation is when the function is rotated about some axis by some degree.
Investigate the function of a line, y = x:
Investigate the function parabola, y = x^2:
STOP
Why do you think we do the opposite motion when the function translates along the x axis? Hint: Look at . Notice that when the graph moves along the positive x direction the function looks like (x - h) but when the function moves in the negative x direction the function looks like (x + h). Why do you think this happens?