PIECEWISE

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
:
x & mbox{if } x ge 0, \
-x & mbox{if } x le 0.
end{cases}

Other examples are the illustrated function, discontinuous at ''x''₀, 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 is not called "piecewise linear" or "piecewise continuous" or "piecewise differentiable" unless the pieces are intervals.

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See also

See also

★ Spline

★ B-spline

★ Piecewise linear function