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Graphing Exponential Functions definitions

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  • Exponential Function
    A mathematical expression where a constant base is raised to a variable exponent, producing rapid growth or decay.
  • Parent Function
    The simplest form of a function in a family, serving as the base for transformations and comparisons.
  • 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 expression.
  • 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.
  • Range
    The set of all possible output values (y-values) that an exponential function can produce, often determined by the asymptote.
  • Transformation
    An operation such as shifting, reflecting, or stretching that alters the position or shape of a function's graph.
  • Reflection
    A transformation producing a mirror image of a graph over a specific axis, determined by the sign and position of a negative.
  • Horizontal Shift
    A transformation moving the graph left or right, determined by the value added or subtracted inside the function's argument.
  • Vertical Shift
    A transformation moving the graph up or down, determined by the value added or subtracted outside the function.
  • Continuous Function
    A function whose graph has no breaks, jumps, or holes, allowing it to be drawn without lifting the pencil.
  • One-to-One Function
    A function where each input corresponds to a unique output, passing the horizontal line test.
  • Horizontal Line Test
    A method for determining if a function is one-to-one by checking if any horizontal line crosses the graph more than once.
  • End Behavior
    The description of how a function's values behave as the input approaches positive or negative infinity.