MATH 2412 – Precalculus
Piecewise Function Exercises
0 if t < 0
1. The Heaviside Function H(t) is defined by H(t) = 
.
1 if t ≥ 0
(a) Graph y = H(t) .
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(b) Graph y = H(t − 3) .
(c) Graph y = H(t) − 3 .
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x −2
2
€
 x − 2 if x ≠€
2. (a) Graph y = 

if x = 2
0
1
€
 2 if x ≠ 0
3. (a) Graph y =  x

 0 if x = 0
x −2
if x ≠ 2
€
x −2
(b) Graph y = 

if x = 2
1
€
4. (a) Write f (x) = 2x − 6 as a piecewise function. (b) Graph f (x) .
€
5. €
(a) Write g(x) = x 2 − x − 6 as a piecewise function.€ (b) Graph g(x) .
6. €
(a) Write h(x) =
x+3
€
as a piecewise function. (b) Graph
h(x) .
x+3
8. Write the equation for the piecewise function whose
€
€ is shown.
graph
y
1
1
x