f is a piecewise smooth funtion on [a,b] if f and f ' are piecewise continuous on [a,b]
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A piecewise defined function is a function which is defined symbolically using two or more formulas
All differentiable functions need be continuous at least.
A piecewise function is a function defined by two or more equations. A step functions is a piecewise function defined by a constant value over each part of its domain. You can write absolute value functions and step functions as piecewise functions so they're easier to graph.
It could represent a point whose coordinates do satisfy the requirements of the function.
One such function is [ Y = INT(x) ]. (Y is equal to the greatest integer in ' x ')