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There are four main types of transformations: translation, rotation, reflection and dilation.
There are three basic rigid transformations: reflections, rotations, and translations. Reflections reflect the shape across a line which is given. Rotations rotate a shape around a center point which is given. Translations slide or move a shape from one place to another.
Transformation involves moving an object from its original position to a new position. The object in the new position is called the image. Each point in the object is mapped to another point in the image. The following figures show the four types of transformations: Translation, Reflection, Rotation, and Dilation.
A function transformation takes whatever is the basic function f (x) and then “transforms” it (or “translates” it), which is a fancy way of saying that you change the formula a bit and thereby move the graph around. Moving the function down works the same way. F (x) b is f (x) moved down b units.
2:00 7:48 Suggested clip Standard/General Form to Transformational Form of a Quadratic YouTubeStart of suggested client of suggested clip Standard/General Form to Transformational Form of a Quadratic
Start with parentheses (look for possible horizontal shift) (This could be a vertical shift if the power of x is not 1.) Deal with multiplication (stretch or compression) Deal with negation (reflection) Deal with addition/subtraction (vertical shift)
To write a rule for this reflection you would write: axis(x, y) (x, y). Notation Rule A notation rule has the following form raise B = axis(x, y) (x, y) and tells you that the image A has been reflected across the y-axis and the x-coordinates have been multiplied by -1.

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