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Transformation

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College Algebra

Definition

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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5 Must Know Facts For Your Next Test

  1. A vertical translation moves a graph up or down without changing its shape.
  2. A horizontal translation shifts a graph left or right and is represented by adding or subtracting inside the function's argument.
  3. Reflections flip a graph over a specific axis; reflecting over the x-axis involves multiplying the function by -1.
  4. Vertical stretches and compressions involve multiplying the entire function by a constant factor greater than 1 (stretch) or between 0 and 1 (compression).
  5. Combined transformations can be applied in sequence; for example, reflecting followed by translating.

Review Questions

  • What effect does adding a constant outside of the function have on its graph?
  • How would you reflect a function \( f(x) \) over the y-axis?
  • Describe how you would vertically stretch the graph of \( f(x) \) by a factor of 3.

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