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A function whose formula is different for different values of the argument. For example:

       {  -1     x is less than 0
f(x) = {   0     x = 0
       {   1     x is greater than 0

is a piecewise function that returns -1 if x is negative, 0 if x = 0, and 1 if x is positive (this is, incidentally, the sign function on some calculators and in some programming languages).

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