Problem 21-2    Source:   Problem elaborated by the author of the site.

Sketch the waveform of the function defined as

Solution of the Problem 21-2

In the picture to the side we see the representation of the waveforms according to the f(t) of the problem statement. The first installment of f(t) is a step function (illustrated in red). Note that the time shift is represented as -t. Therefore, your amplitude is 2volts from - ∞ to zero time.

The second parcel (illustrated in orange) is also a step function with -3 volts in amplitude and shifted to t = 2 s.

The third installment is a step function with an amplitude of 2 volts and time-shifted in 4 s.

So, doing the algebraic sum of the functions and obeying the displacement times we can plot the resulting waveform as illustrated at the bottom of the figure above.