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Functions definitions

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  • Relation
    A pairing of input and output values, often shown as ordered pairs or points on a graph.
  • Function
    A special relation where each input is linked to at most one output, ensuring unique outputs for every input.
  • Vertical Line Test
    A graphical method to check if a graph represents a function by seeing if any vertical line crosses more than one point.
  • Input
    A value, typically represented by x, that is fed into a relation or function to produce an output.
  • Output
    A value, typically represented by y or f(x), resulting from applying a function or relation to an input.
  • Function Notation
    A way to express functions using f(x) instead of y, highlighting the dependence of outputs on inputs.
  • Domain
    The set of all allowed input values for a function, often determined by restrictions like square roots or denominators.
  • Range
    The set of all possible output values a function can produce, visualized by squishing a graph to the y-axis.
  • Interval Notation
    A concise method using brackets and parentheses to describe sets of numbers, especially domains and ranges.
  • Set Builder Notation
    A notation using inequality symbols to specify sets, often used for domains and ranges with restrictions.
  • Constant Function
    A function where every input yields the same output, resulting in a horizontal line on a graph.
  • Identity Function
    A function where the output equals the input, producing a diagonal line through the origin.
  • Square Function
    A function where outputs are the squares of inputs, forming a parabola with only non-negative outputs.
  • Cube Function
    A function where outputs are cubes of inputs, covering all real numbers for both domain and range.
  • Square Root Function
    A function defined only for non-negative inputs, with outputs as the square roots of those inputs.
  • Cube Root Function
    A function where outputs are cube roots of inputs, allowing all real numbers for both domain and range.