Piecewise Function vs Regular Function

Question

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.

Answer 1

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.