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Piecewise
Function defined by multiple sub-functions / From Wikipedia, the free encyclopedia
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In mathematics, a piecewise-defined function (also called a piecewise function, a hybrid function, or definition by cases) is a function whose domain is partitioned into several intervals ("subdomains") on which the function may be defined differently.[1][2][3] Piecewise definition is actually a way of specifying the function, rather than a characteristic of the resulting function itself.
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A function property holds piecewise for a function, if the function can be piecewise defined in a way that the property holds for every subdomain. Examples of functions with such piecewise properties are piecewise constant functions, piecewise linear functions (see the figure), piecewise continuous functions, piecewise smooth functions, and piecewise differentiable functions.