Functions Transformations/Translations/Dilations/Reflections/Rotations

The Basics
What is a Translation? A translation moves the graph up, down, and side to side. [br][br]What is a Dilation? A dilation makes the function skinnier or larger. [br][br]What is a Reflection? A reflection is a mirror image. This flips the function over the x or y axes.[br][br]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. [br]
Investigate the function of a line, y = x:
Investigate the function parabola, y = x^2:
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Why do you think we do the opposite motion when the function translates along the x axis? [br][br]Hint: Look at [math]\left(x-h\right)^2[/math]. 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:
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Information: Functions Transformations/Translations/Dilations/Reflections/Rotations