f(t) = u(t) + (1 − t) • u(t − 1) + (t − 2) • u(t − 2)

Expanding where possible:

= u(t) + u(t − 1) − t • u(t − 1) + t • u(t − 2) − 2 • u(t − 2)

= [u(t) − u(t − 1)] + 2 • u(t − 1) − t • [u(t − 1) − u(t − 2)] − 2 • u(t − 2)

[We wrote u(t − 1) as − u(t − 1) + 2 • u(t − 1), to get the expression in the form we need.]

= [u(t) − u(t − 1)] + 2 • [ u(t − 1) − u(t − 2)] − t • [u(t − 1) − u(t − 2)]

[We simply moved the last term.]

= 1 • [u(t) − u(t − 1)] + (2 − t) • [ u(t − 1) − u(t − 2)]

[Collecting like terms.]

From this expression, we can graph the function. It has value:

1 between 0 < t < 1

2 − t between 1 < t < 2

0 thereafter

NOTE: We could have obtained the graph of f(t) = u(t) + (1 − t) • u(t − 1) + (t − 2) • u(t − 2) by adding ordinates of the 3 parts as follows:

u(t) → red

(1 − t) • u(t − 1) → green

(t − 2) • u(t − 2) → magenta

The blue part is the answer.