Common Functions definitions Flashcards
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.