Constant function

A function that maps every element of its domain to one fixed value in its codomain. Its output does not depend on its input.

Function (mathematics): A relation that assigns each element of a domain exactly one element of a codomain. A constant function is a special case of a function, with the same assigned output everywhere.
Zero function: A function whose value is zero at every point of its domain. It is the constant function singled out as the additive identity in many function spaces.
Constant polynomial: A polynomial consisting only of a fixed coefficient, including the zero polynomial. It is the polynomial instance of a constant function, evaluated on its usual number domain.
Identity function: A function that maps every element of a set to itself. Unlike a constant function, its output usually varies with the input.
Domain of a function: The set of inputs for which a function is defined. The fixed-output condition must hold for every element in this set.
Derivative: A measure of a function’s instantaneous rate of change with respect to its input. Every differentiable constant function has derivative zero throughout its domain.
Indicator function: A function that takes value one on a specified set and zero outside it. It is constant on each of two regions, but generally not across its entire domain.
Linear function: A function between vector spaces that preserves addition and scalar multiplication. A constant function between vector spaces is linear only in the zero-valued case.
Codomain: The specified set in which a function’s outputs are required to lie. The constant value must belong to this set, even if other codomain values are unused.
Integral: A mathematical operation that accumulates values over an interval or domain. Integrating a constant over an interval multiplies its value by the interval’s length.

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