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Introduction to 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.
  • Polynomial Function
    An expression involving variables raised to whole number powers, with the variable in the base rather than the exponent.
  • Base
    A constant positive number, not equal to 1, that is repeatedly multiplied in an exponential expression.
  • Exponent
    A value, often a variable, indicating how many times the base is used as a factor in repeated multiplication.
  • Variable
    A symbol, such as x or y, representing a quantity that can change within a mathematical expression.
  • Constant
    A fixed value that does not change, often serving as the base in exponential functions.
  • Fractional Base
    A base expressed as a fraction, allowed in exponential functions if it is constant and positive.
  • Negative Exponent
    An exponent less than zero, resulting in the reciprocal of the base raised to the corresponding positive power.
  • Caret Key
    A calculator symbol (^) used to indicate exponentiation, allowing entry of powers for computation.
  • Evaluation
    The process of substituting specific values for variables in a function to determine its output.
  • Growth
    A pattern in exponential functions where values increase rapidly as the exponent increases.
  • Decay
    A pattern in exponential functions where values decrease rapidly, often when the base is between 0 and 1.
  • Power
    The complete expression in the exponent, which may include variables and constants, indicating the degree of exponentiation.
  • Reciprocal
    A value obtained by inverting a number, commonly resulting from negative exponents in exponential expressions.
  • Parentheses
    Symbols used in calculations to group terms, ensuring correct order of operations when entering exponents.