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Introduction to Inverse Functions definitions

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  • Function
    A relation where each input is paired with at most one output, ensuring no input connects to multiple outputs.
  • One-to-One Function
    A function where each output is paired with at most one input, preventing repeated outputs from different inputs.
  • Inverse Function
    A function that reverses the original mapping, swapping inputs and outputs, denoted with a superscript negative one.
  • Ordered Pair
    A set of two values representing input and output, typically written as (x, y) for functions.
  • Input
    The value from the domain that is mapped to an output in a function, often represented as x.
  • Output
    The value from the range that results from applying a function to an input, often represented as y.
  • Domain
    The complete set of possible input values for a function, which becomes the range in its inverse.
  • Range
    The complete set of possible output values for a function, which becomes the domain in its inverse.
  • Correspondence Diagram
    A visual representation showing how inputs and outputs pair in a function, using arrows between bubbles.
  • Horizontal Line Test
    A graphical method to verify one-to-one status by checking if any horizontal line crosses more than one point.
  • Vertical Line Test
    A graphical method to confirm a relation is a function by ensuring vertical lines cross at most one point.
  • Notation
    A symbolic representation, such as f⁻¹, used to distinguish inverse functions from exponents.
  • Relation
    A set of ordered pairs, not necessarily a function, where inputs may connect to multiple outputs.
  • Mapping
    The process of associating each input with an output, visualized in diagrams or ordered pairs.
  • Superscript Negative One
    A symbol placed above a function name to indicate its inverse, not to be confused with an exponent.