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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
    A mathematical expression involving variables raised to whole number powers, with coefficients, summed together.
  • Base
    A constant positive number, not equal to one, that is repeatedly multiplied in an exponential expression.
  • Exponent
    A power containing a variable, indicating how many times the base is used as a factor in an exponential function.
  • Variable
    A symbol, often x or y, representing a value that can change within a mathematical function or expression.
  • Constant
    A fixed value that does not change, such as the base in an exponential function.
  • Fractional Base
    A base in an exponential function that is a positive fraction, like 2/3, meeting all criteria for validity.
  • Negative Exponent
    An exponent less than zero, resulting in the reciprocal of the base raised to the corresponding positive power.
  • Carat Key
    A calculator button (^) used to input exponents, allowing entry of powers for evaluation.
  • 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 zero and one.
  • Evaluation
    The process of substituting specific values for variables in a function to calculate a numerical result.
  • Reciprocal
    A value obtained by inverting a number, such as 1 divided by the original number, often seen with negative exponents.
  • Parentheses
    Symbols used in calculations to group terms, ensuring correct order of operations, especially in exponentiation.
  • Power
    The complete expression in the exponent position, which may include variables and constants, determining the operation on the base.