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