Transformation refers to any operation that moves or changes a function in some way. Common transformations include translations, dilations, reflections, and rotations.
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A vertical translation moves a graph up or down without changing its shape.
A horizontal translation shifts a graph left or right and is represented by adding or subtracting inside the function's argument.
Reflections flip a graph over a specific axis; reflecting over the x-axis involves multiplying the function by -1.
Vertical stretches and compressions involve multiplying the entire function by a constant factor greater than 1 (stretch) or between 0 and 1 (compression).
Combined transformations can be applied in sequence; for example, reflecting followed by translating.