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A piecewise function is usually defined by more than one formula: a fomula for each interval. Example 1: f( x ) = - x if x <= 2 = x if x > 2 What the above says is that if x is smaller than or equal to 2, the formula for the function is f( x ) = -x and if x is greater than 2, the formula is f( x ) = x.
Piecewise functions are functions that have more than one part, the most common of which is the absolute value function. Each piece of the function has a well-defined domain, or x-value. To graph a piecewise function, you need only to be sure that you have properly defined the area for each graph and then only place the graph in that area.