Piece-wise defined functions
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A typical introduction of piece-wise defined functions in a calculus textbook looks something like this: there are functions that take on different formulas depending on the intervals (pieces) of their domains, for example: [math]\displaystyle{ f(n) = \begin{cases} x^2, & \mbox{if }x\le 1 \\ 3-2x, & \mbox{if }x \gt 1 \end{cases} }[/math]
(examples may vary).
- Water density :::
Below we try to give a bit more motivation to piece-wise functions (which is not just a nuance for students, but rather indispensable tool in mathematics and applications).
Ball
Pool table
Water freezing