Real-valued function

A function that assigns a real number to every element of its domain, which may consist of numbers, vectors, or other objects.

Function: A mapping that assigns exactly one output to each element of a domain. Real-valued functions are functions distinguished by their real-number outputs.
Limit of a function: A value that function outputs approach as inputs approach a specified point. Limits define continuity and local behavior for real-valued functions.
Objective function: A function assigning a numerical score to each candidate solution in an optimization problem. Optimization often seeks inputs where a real-valued objective reaches an extreme.
Complex-valued function: A function whose outputs are complex numbers. Its outputs extend beyond the real numbers by including an imaginary component.
Real number: A number on the continuous number line, including rational and irrational numbers. Every output of a real-valued function belongs to this number system.
Continuity: A property of a function whose values vary without jumps at a point or throughout a domain. Real-valued functions can be classified by where their outputs change continuously.
Probability density function: A nonnegative function whose integral over a region gives the probability of a continuous random variable lying there. It assigns real-valued densities to possible outcomes, rather than probabilities to individual points.
Vector-valued function: A function whose outputs are vectors rather than single numbers. It generalizes real-valued functions to outputs with multiple coordinates.
Domain of a function: The set of inputs for which a function is defined. Its elements need not be real numbers, even when every output is.
Derivative: The instantaneous rate of change of a function with respect to its input. For real-valued functions, derivatives quantify local output change when the domain supports differentiation.

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