MHB Write the piecewise function in terms of unit step functions.

[shamieh]

Write the piecewise function
\[ f(t) = \begin{cases}
2t, & 0\leq t < 3 \\
6, & 3 \le t < 5 \\
2t, & t \ge 5 \\
\end{cases}
\]
in terms of unit step functions.

So here is what i;ve got just guessing , I don't think I'm correct. I really need some help. But I got:

$f(t) = 2t[u(t-0) - u(t-3)] + 6[u(t-3) - u(t-5)] + 2t[u(t-5) - u(t - \infty)]$

Which becomes

$f(t) = 2t[u(t) - u(t-3)] + 6[u(t-3) - u(t-5)] + 2t[u(t-5)]$

 

[Ackbach]

Looks good to me!