Graph the following and determine the unit step function:
$$f(t) = \begin{cases}5 ,& 0 \leq t < 8 \\-4 ,& \ t \ge 8\end{cases}$$
Our class has just started doing this topic, so apologies if this must be a very simple question for you. I drew a graph of what I think it should look like:
And this is what I think the unit step function should look like
$$f(t) = 5u(t) - 9u(t-8)$$
That would make sense to me or is it:
$$f(t) = 5u(t) - 4u(t-8)$$
If someone could help I would be grateful
In general, if:
$$f(t)= \left\{\begin{array} fg(t) &0 \le t < a\\h(t) &t \ge a \end{array}\right.$$
then:
$$f(t) = g(t) - g(t)u(t-a) + h(t) u(t-a)$$
For your particular problem, we have:
$$f(t) = \begin{cases}5 ,& 0 \leq t < 8 \\-4 ,& \ t \ge 8\end{cases}$$
Using unit step functions, we can write this as:
$$f(t) = 5 - 5 u(t-8) - 4 u(t-8) = 5 - 9u(t-8)$$
Your plot is correct for the range you plotted, but also realize that it is zero for $t \le 0$.