In mathematics, a constant function is a function whose values do not vary and thus are constant. For example the function f(x) = 4 is constant since f maps any value to 4. More formally, a function f : A → B is a constant function if f(x) = f(y) for all x and y in A.
Every empty function is constant, vacuously, since there are no x and y in A for which f(x) and f(y) are different when A is the empty set.
In the context of polynomial functions, a non-zero constant function is called a polynomial of degree zero.
A function is said to be identically zero if it takes the value 0 for every argument; it is then trivially a constant function.
Read more about Constant Function: Properties
Famous quotes containing the words constant and/or function:
“Love not me for comely grace,
For my pleasing eye or face,
Nor for any outward part:
No, nor for a constant heart!”
—Unknown. Love Not Me for Comely Grace (l. 1–4)
“The function of the actor is to make the audience imagine for the moment that real things are happening to real people.”
—George Bernard Shaw (1856–1950)