Given a piecewise function, such as
$f(t) = \begin{cases} 2, & \text{if }t \lt a \\ t^2, & \text{if }t \geq a \end{cases}$
Or some other piecewise function, how can we write it in the form $u(t-a)f(t-a)$ for $u(t-a) = \begin{cases} 0, & \text{if }t \lt a \\ 1, & \text{if }t \geq a \end{cases}$
A simple explanation that doesn't involve too much math knowledge is preferable, but I would still like to generalize this across other functions that I may come across.
Thank you.