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Transformations definitions

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  • Transformation
    A change in a function's position or shape, often categorized as a reflection, shift, or stretch.
  • Reflection
    A manipulation where a graph is folded over an axis, resulting in a mirror image across that axis.
  • Shift
    A movement of a graph to a new location without altering its overall shape.
  • Stretch
    A modification that expands or compresses a graph vertically, altering its steepness.
  • Function Notation
    A symbolic way to represent transformations, such as negatives for reflections or constants for stretches.
  • Vertical Stretch
    An adjustment where a graph is pulled away from or pushed toward the x-axis by a constant factor.
  • 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 outside the function.
  • Constant
    A fixed value multiplied by a function, responsible for stretching or compressing the graph.
  • Axis
    A reference line, such as the x-axis, used for folding or reflecting a graph.
  • Origin
    The point (0,0) on a graph, often used as a reference for shifts and transformations.
  • Graph
    A visual representation of a function, used to illustrate the effects of transformations.
  • Absolute Value Function
    A V-shaped graph commonly used to demonstrate transformations like shifts, reflections, and stretches.
  • Multiple Transformations
    A situation where more than one change, such as a reflection and a stretch, occurs simultaneously in a function.