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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 the output equals the input for all real numbers, forming 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 extending in all directions.
  • Square Root Function
    A function defined only for non-negative inputs, producing outputs from zero to positive infinity.
  • Cube Root Function
    A function that allows all real inputs, including negatives, and outputs all real numbers.
  • Domain
    The complete set of possible input values for a function, often described using intervals.
  • Range
    The set of all possible output values a function can produce, determined by the function's rule.
  • Parabola
    A symmetric, bowl-shaped curve representing the graph of a quadratic function.
  • Real Numbers
    All numbers on the continuous number line, including negatives, zero, and positives.
  • Horizontal Line
    A straight line with constant y-value, representing the graph of a constant function.
  • Origin
    The point (0,0) on a coordinate plane where the x-axis and y-axis intersect.
  • Quadratic Function
    A function where the highest power of the variable is two, typically forming a parabola.
  • Interval Notation
    A mathematical notation used to describe the domain or range of a function using brackets and parentheses.
  • Graph
    A visual representation of a function, showing the relationship between input and output values.