The step function ua (t) is defined as follows:

0 t < a
ua (t) = 
1 t ≥ a


0 t < 0
Setting a = 0 gives: u0 (t) = 
1 t ≥ 0

u0 (t) is sometimes denoted as h(t) (h for Heaviside).
Note that h(t − a)
Graph f (t) = 1 − u2 (t)
Graph f (t) = u3 (t) − u5 (t)
Graph f (t) = t 2u1 (t)
Graph f (t) = (t − 1) 2u1 (t)
From your notes (p19):
“Hence, given a function f (t), defined for t ≥ 0, the graph of the
function f (t−a)ua (t) consists of the graph of f (t) translated through
a distance a to the right with the portion from 0 to a ’turned off’, i.e.
set equal to zero.”
Graph f (t) = et−2u2 (t)
Here’s a graph that turns on at t = 2 and turns off at t = 3. How is it
expressed in terms of step functions?
A
(1 − t)u2 (t) − u3 (t)
B
(1 − t)[u2 (t) − u3 (t)]
C
(3 − t)u2 (t) − u3 (t)
D
(3 − t)[u2 (t) − u3 (t)]


0
0≤t<1






t − 1 1 ≤ t < 3
Write the function f (t) = 
in terms of unit step


1
3≤t≤4





0
t>4

functions.