What a piecewise function is
A piecewise function is given by several expressions, each valid only on its own subset of the domain. At boundaries you specify whether the endpoint belongs to the left or right piece (square vs round bracket in notation).
In grade 9 you often see line + parabola or two quadratic pieces on different rays and segments.
The domain of the function is the union of the domains of the pieces, minus points where a formula is undefined
At a "junction" it helps to evaluate limits from the left and right — at least numerically — for continuity
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