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Transformations definitions

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  • Transformation
    Any manipulation that changes the position or shape of a function's graph, such as reflection, shift, or stretch.
  • Reflection
    A flip of a graph over a specific axis, resulting in a mirror image and changing the sign of certain values.
  • Shift
    A movement of a graph horizontally, vertically, or both, relocating every point without altering the graph's shape.
  • Stretch
    An alteration that expands a graph away from an axis, making it appear taller or wider depending on the direction.
  • Compression
    A transformation that squeezes a graph toward an axis, making it appear shorter or narrower.
  • Horizontal Shift
    A translation of a graph left or right, determined by the value inside the function's argument.
  • Vertical Shift
    A translation of a graph up or down, determined by a value added or subtracted outside the function.
  • Vertical Stretch
    A transformation that multiplies all y-values by a constant greater than one, making the graph taller.
  • Vertical Compression
    A transformation that multiplies all y-values by a constant between zero and one, making the graph shorter.
  • Horizontal Stretch
    A transformation that multiplies the input by a constant between zero and one, spreading the graph wider.
  • Horizontal Compression
    A transformation that multiplies the input by a constant greater than one, squeezing the graph closer to the y-axis.
  • Domain
    The complete set of possible input values for a function, which may change after a transformation.
  • Range
    The complete set of possible output values for a function, which can be altered by transformations.
  • Function Notation
    A symbolic way to represent transformations, such as f(x-h)+k for shifts or cf(x) for stretches.
  • Combination Transformation
    A scenario where multiple transformations, like reflection and shift, are applied to a function simultaneously.