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In mathematics, a piecewise-defined function (also called a piecewise function) is a function which is defined by multiple subfunctions, each subfunction applying to a certain interval of the main function's domain (a subdomain). Piecewise is actually a way of expressing the function, rather than a characteristic of the function itself, but with additional qualification, it can describe the nature of the function. For example, a piecewise polynomial function: a function that is a polynomial on each of its subdomains, but possibly a different one on each.
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 subdomain, even though the whole function may not be differentiable at the points between the pieces. In convex analysis, the notion of a derivative may be replaced by that of the subderivative for piecewise functions. 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.-source wikipedia
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In this clip we go over how to graph a piece wise defined function comprised of two linear functions. We start out by going over the steps or strategies for graphing piecewise defined functions.
Steps for Graphing Piecewise functions(How to graph):
1) Plan: Use a number line to plan out which function goes where on the coordinate plane.
2) Graph Partition(s) & Label: On the coordinate system graph your partition(s) and label the sectioned planes accordingly using your set up in 1.
3)Graph each Piece: Graph the line of each function in their respective planes paying close attention to inclusion and exclusion at boundaries.
A piecewise function is a function made up of two or more pieces of functions defined on specified domains (intervals) of the piecewise function.
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