In mathematics, a constant function is a function whose (output) value is the same for every input value.
y(x) is 4 regardless of the input value
c = 4. The
domain of this function is the set of all
real numbers. The
image of this function is the
singleton set
y(0) = 4,
x is input, the output is
(0, c). In the context of a
polynomial in one variable
c is nonzero. This function has no intersection point with the
f(x) = 0 is the identically zero function. It is the (trivial) constant function and every x-axis in the plane. Its graph is symmetric with respect to the
(x↦c)′=0. The converse is also true. Namely, if y is a constant function. For example, given the constant function y(x) = -\\sqrt{2}</math>."}},"i":0}}]}'>f is a lattice, then X, which implies that it is also idempotent.
It has zero slope or gradient.
Every constant function between topological spaces is continuous.
A constant function factors through the one-point set, the terminal object in the category of sets. This observation is instrumental for F. William Lawvere's axiomatization of set theory, the Elementary Theory of the Category of Sets (ETCS).
For any non-empty X→Y. For any Y, there is a unique function x∈X. Conversely, if a function x,x′∈X, X1, or hom set λ:1×X≅X≅X×1:ρ natural in p2 the ordered pairs x, where