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Function Notation definitions

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  • Function
    A mathematical rule assigning each input exactly one output, often written as an equation or set of ordered pairs.
  • Function Notation
    A symbolic way to represent the output of a function for a specific input, typically written as f(x), g(x), or h(x).
  • Input
    A value substituted into a function, usually corresponding to the x-value in equations, ordered pairs, or graphs.
  • Output
    The result produced by a function after substituting the input, often matching the y-value in equations or graphs.
  • Ordered Pair
    A set of two values, usually written (x, y), representing input and output in a function or relation.
  • Expression
    A mathematical phrase within a function that determines how the input is transformed to produce the output.
  • Graph
    A visual representation of a function, showing the relationship between inputs and outputs as points or curves.
  • Equation
    A mathematical statement showing the relationship between variables, often used to define a function.
  • x-value
    The horizontal coordinate in an ordered pair or graph, representing the input for a function.
  • y-value
    The vertical coordinate in an ordered pair or graph, representing the output from a function.
  • Function Name
    A letter or symbol, such as f, g, or h, used to identify a specific function in notation.
  • Parentheses
    Symbols used in function notation to enclose the input value, indicating which value is being substituted.
  • Simplification
    The process of reducing a mathematical expression to its simplest form after substituting the input.
  • Curve
    A continuous line on a graph representing the set of all outputs for corresponding inputs in a function.
  • Polynomial
    An algebraic expression consisting of terms with variables raised to whole number powers, often used in function definitions.