Constant function

The domain of this function is the set of all real numbers.

The image of this function is the singleton set {4}.

The independent variable x does not appear on the right side of the function expression and so its value is "vacuously substituted"; namely y(0) = 4, y(−2.7) = 4, y(π) = 4, and so on.

[1] The graph of the constant function y = c is a horizontal line in the plane that passes through the point (0, c).

[2] In the context of a polynomial in one variable x, the constant function is called non-zero constant function because it is a polynomial of degree 0, and its general form is f(x) = c, where c is nonzero.

This function has no intersection point with the x-axis, meaning it has no root (zero).

[4] In the context where it is defined, the derivative of a function is a measure of the rate of change of function values with respect to change in input values.

For functions between preordered sets, constant functions are both order-preserving and order-reversing; conversely, if f is both order-preserving and order-reversing, and if the domain of f is a lattice, then f must be constant.