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:


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?

Investigate the absolute value function, y = |x|:

Investigate the square root function, y = x^1/2:

Investigate the cubic function below, y = x^3: