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Graphing Exponential Functions definitions

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  • Exponential Function
    A mathematical relationship where a constant base is raised to a variable exponent, producing rapid growth or decay.
  • Base
    The constant value in an exponential expression that is repeatedly multiplied as the exponent changes.
  • Exponent
    The variable or number indicating how many times the base is used as a factor in an exponential function.
  • Horizontal Asymptote
    A horizontal line that a graph approaches but never touches, indicating the function's end behavior.
  • Domain
    The complete set of possible input values (x-values) for which an exponential function is defined, always all real numbers.
  • Range
    The set of possible output values (y-values) for an exponential function, determined by the position of the asymptote.
  • Parent Function
    The simplest form of an exponential function, serving as the starting point for transformations.
  • Transformation
    An operation such as shifting, reflecting, or stretching that alters the position or shape of a graph.
  • Reflection
    A transformation producing a mirror image of a graph over the x-axis or y-axis, depending on the sign placement.
  • Horizontal Shift
    A transformation moving the graph left or right, determined by changes inside the function's exponent.
  • Vertical Shift
    A transformation moving the graph up or down, determined by values added or subtracted outside the function.
  • Continuous Graph
    A graph with no breaks or gaps, where every point between two values is included.
  • One-to-One Function
    A function where each input corresponds to exactly one output, passing the horizontal line test.
  • End Behavior
    The description of how a function behaves as the input values approach positive or negative infinity.
  • Test Point
    A specific coordinate used to help plot or transform a graph, often derived from the parent function.