Making a Piecewise Function a Single Function Is there a way to turn a piecewise function into one function. For example:
$$\ f(x)=\begin{cases} g(x) & \text{if $a≤x<b $} \\ h(x) & \text{if $b≤x≤d$} \end{cases}$$
(Can you use the Heaviside Step Function? $\theta(x))$

Yes, just make a pulse with the step function $$\displaylines{
  f(x) = g(x)\left( {\theta (x - a) - \theta (x - b)} \right) \cr 
   + h(x)\left( {\theta (x - b) - \theta (x - d)} \right) \cr} $$
