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? $\theta(x))$

You can rewrite $f(x)$ as $$f(x)=\chi_{[a,b)}(x)g(x)+\chi_{[c,d)}(x)h(x),$$ where $\chi_{[a,b)}(x)$ is $1$ if $x\in[a,b)$ and $0$ otherwise.
