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We can create new functions from existing ones in several ways. Left case: All $n-1$ maximum terms vanish. We can create new functions from existing ones in several ways. About Statistics Number Theory Java Data Structures Precalculus Calculus Piecewise Functions. Update: I tried a different decomposition for $f$, but the "dynamic" approach that user Carsten Schultz posted turned out to be easier so far. This can be exploited to combine these functions in such a way that a decision with at least $n$ cases can be realized to deal with the $n$ continous pieces of the piecewise linear function. The basic mechanism at work is that functions such like $|.|$ or $\min$ or $\max$ or $\Theta$ realize case decisions depending on their argument, together with the closedness of linear functions regarding linear combinations. Absolute Value Functions and Piecewise Functions Graphing Abs Value.pdf.