Piecewise- Defined Functions

A function f may involve two or more expressions or formulas, with each formula defined on different parts of the domain of f. A function defined in this manner is called a piecewise- defined function. Piecewise functions are written using the common functional notation, where the main part of the function is an array of functions and associated subdomains. Most importantly, there must be a finite number of subdomains, each of which must be an interval, in order for the overall function to be called "piecewise". For absolute value piecewise functions all values of x less than zero, the first function (−x) is used. Which cancels the sign of the input value, making negative numbers positive. For all values of x greater than or equal to zero, the second function (x) is used, which evaluates trivially to the input value itself.

 

Here is a picture of a piecewise function being graphed.