Piecewise Functions - Maple Help

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Piecewise Functions

Main Concept

A function whose formula is different on different parts of its domain is called a piecewise function. Such a function is commonly (but not necessarily) written using a case structure:

$f\left(x\right)=\left\{\begin{array}{cc}{f}_{1}\left(x\right)& {\mathrm{condition}}_{1}\\ {f}_{2}\left(x\right)& {\mathrm{condition}}_{2}\\ {f}_{3}\left(x\right)& {\mathrm{condition}}_{3}\\ ...& ...\end{array}\right\$

The conditions should be mutually exclusive. That is, at any given value of $x$ at most one of the conditions can be true. The value of the function is then the value of the subformula corresponding to the true condition.

Examples

 $g\left(x\right)=\left\{\begin{array}{cc}-1-x& x<-2\\ \mathrm{sin}\left(x\right)& -2\le x<1\\ \frac{1}{{x}^{2}}& 1\le x\end{array}\right\$

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