Everything about Piecewise Defined Function totally explained
In
mathematics, a
piecewise-defined function f(
x) of a
real variable x is a
function whose definition is given differently on disjoint subsets of its
domain.
A common example is the
absolute value function, given by
»
Other examples are the illustrated function, discontinuous at
x0, and the
Heaviside step function, a
piecewise linear function which is discontinuous at 0.
The word
piecewise is also used to describe any property of a piecewise-defined function that holds for each piece but may not hold for the whole
domain of the function. A function is
piecewise differentiable or
piecewise continuously differentiable if each piece is differentiable throughout its domain. Although the "pieces" in a piecewise definition need not be
intervals, a function isn't called "piecewise linear" or "piecewise continuous" or "piecewise differentiable" unless the pieces are intervals.
See also
Further Information
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