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Transformations

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Termini in questo insieme (19)

  • What is a transformation of a function?
    A transformation occurs when a function is moved or changed in position and/or shape.
  • Name the three main types of function transformations.
    Reflection, Shift, and Stretch.
  • What does a reflection transformation do to a function?
    A reflection folds the function over the x-axis or y-axis, changing the sign of x or y values.
  • How is a reflection over the x-axis represented mathematically?
    Reflection over the x-axis is represented as \(-f(x)\).
  • How is a reflection over the y-axis represented mathematically?
    Reflection over the y-axis is represented as \(f(-x)\).
  • What changes sign during a reflection over the x-axis?
    The y-values change sign during a reflection over the x-axis.
  • What changes sign during a reflection over the y-axis?
    The x-values change sign during a reflection over the y-axis.
  • What is a shift transformation?
    A shift moves a function horizontally and/or vertically from its original position.
  • How does the graph shift for \(f(x) + k\)?
    The graph shifts up by k units.
  • How does the graph shift for \(f(x) - k\)?
    The graph shifts down by k units.
  • How does the graph shift for \(f(x - h)\)?
    The graph shifts right by h units.
  • How does the graph shift for \(f(x + h)\)?
    The graph shifts left by h units.
  • What is the general form of a shift transformation?
    The general form is \(f(x - h) + k\), where h is horizontal shift and k is vertical shift.
  • What is a stretch or shrink transformation?
    A stretch or shrink occurs when a constant c multiplies the function inside or outside, changing its shape.
  • How is a vertical stretch represented?
    A vertical stretch is represented as \(c \, \cdot \, f(x)\) with c > 1.
  • How is a vertical shrink represented?
    A vertical shrink is represented as \(c \, \cdot \, f(x)\) with 0 < c < 1.
  • How is a horizontal stretch represented?
    A horizontal stretch is represented as \(f(c \, x)\) with 0 < c < 1.
  • How is a horizontal shrink represented?
    A horizontal shrink is represented as \(f(c \, x)\) with c > 1.
  • How can transformations affect the domain and range of a function?
    Transformations can change the domain and range of a function, which can be found by analyzing the new graph.