Piecewise
From Wikipedia, the free encyclopedia
In mathematics, a piecewise-defined function f(x) of a real variable x is a function whose definition is given differently on disjoint intervals of its domain.
A common example is the absolute value function.
Other examples are the illustrated function, discontinuous at x0, and the Heaviside step function, a piecewise linear function discontinuous at 0. The word piecewise is also used to describe any property of a piecewise function that holds for each piece but may not hold for the whole domain of the function. The major structure of the definition of a piecewise function is an if-then-else clause.
A synonym for piecewise is piecewise continuous. A function is piecewise differentiable or piecewise continuously differentiable if each piece is differentiable throughout its domain.
