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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.
Illustration of the piecewise cubic basis functions associated with nodes in element 1. We see that all the piecewise linear basis functions have the same âhatâ shape. They are naturally referred to as hat functions, also called chapeau functions.