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Common Functions definitions

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  • Constant Function
    A function where every input yields the same output value, represented by a horizontal line on the graph.
  • Identity Function
    A function where each input value is matched to itself, resulting in a straight line through the origin.
  • Square Function
    A function where each input is raised to the second power, producing a parabola opening upwards.
  • Cube Function
    A function where each input is raised to the third power, resulting in a curve that passes through the origin and extends in all directions.
  • Square Root Function
    A function that outputs the non-negative root of the input, defined only for non-negative values and increasing slowly.
  • Cube Root Function
    A function that outputs the real root of the input, defined for all real numbers and symmetric about the origin.
  • Domain
    The complete set of input values for which a function is defined, often spanning all real numbers or a restricted interval.
  • Range
    The set of all possible output values a function can produce, determined by the function's rule and graph.
  • Parabola
    A symmetric, bowl-shaped curve representing the graph of a quadratic function, opening either upward or downward.
  • Real Numbers
    All numbers on the continuous number line, including both positive and negative values, zero, and irrational numbers.
  • Horizontal Line
    A straight line on a graph with constant y-value, representing a function with no change in output.
  • Origin
    The point (0,0) on a coordinate plane where the x-axis and y-axis intersect.
  • Output
    The result produced by a function after substituting an input value, also known as the dependent variable.
  • Input
    The value substituted into a function, determining the corresponding output, also called the independent variable.