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I'm into graphing functions and I'm currently working on some project of mine. I'm a little confused, what's the main distinction of a Piecewise Function with just a Regular / $f(x)$ Function? I mean, most Piecewise functions posses the same format of equations with an $f(x)$ Function.

Xander Henderson
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Justin Gabriel
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  • What is exactly don't you understand? A piecewise function is just a function which is made up of multiple functions and is defined by exactly one of them in every part of its domain. f(x) is just the notation for a function. It can also be used for a piecewise function. – Akul Singhal Jun 19 '20 at 04:57
  • There are piecewise continuous functions and piecewise smooth functions etc. but piecewise function is a nonsense term which seems to have some popularity e.g. on this site. There is no need for the term because, as you say, a "piecewise function" is just a function. – bof Jun 19 '20 at 05:15

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Generally a piece-wise function has at least one jump discontinuity in it. For example $F(x) =1$ is a "regular" function as you refer to it; whereas $G(x)= \begin{cases} -1 & x< 0 \\ 0 & 0\leq x\leq 100 \\ 1 & x > 100 \end{cases}$ is piece-wise (it has jump discontinuities at $x=0$ and $x=100$). For more info see the Wikipedia article on piecewise functions.

Mark
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