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Transformations definitions

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  • Transformation
    Alters a function's graph or equation, changing its position or shape through specific manipulations.
  • Reflection
    Creates a mirror image of a graph over an axis, flipping either the y-values or x-values.
  • Shift
    Moves a graph horizontally or vertically, relocating its entire shape to a new position.
  • Stretch
    Expands a graph vertically or horizontally, increasing its height or width based on a constant.
  • Shrink
    Compresses a graph vertically or horizontally, reducing its height or width by a constant factor.
  • Vertical Stretch
    Multiplies the function by a constant greater than one outside, making the graph taller.
  • Vertical Shrink
    Multiplies the function by a constant between zero and one outside, making the graph shorter.
  • Horizontal Stretch
    Multiplies the input by a constant between zero and one inside, making the graph wider.
  • Horizontal Compression
    Multiplies the input by a constant greater than one inside, making the graph narrower.
  • Function Notation
    Represents transformations using symbols like f(x-h)+k or cf(x), indicating shifts and stretches.
  • Domain
    Set of all possible x-values for a function, which can change after a transformation.
  • Range
    Set of all possible y-values for a function, often altered by transformations.
  • Horizontal Shift
    Moves a graph left or right, determined by the value inside the function's argument.
  • Vertical Shift
    Moves a graph up or down, determined by the value added outside the function.
  • Combination Transformation
    Applies multiple transformation rules sequentially, resulting in a new graph and notation.