Algebra II Notes
Piecewise Functions
Piecewise linear functions
Practice 1.5
1. Match the piecewise function with its graph.
2. Which graph represents the piecewise function below?
if x  2
 x,

f ( x )   5,
if  3  x  2
 3 x  2, if x  3

Which function represents the graph below?
Alg II Notes Unit 1.5 Piecewise Functions
Page 1 of 5
Unit 1.5
Algebra II Notes
Piecewise Functions
 x  1,
f ( x)  
 x,
A.
 x,
B. f ( x)  
 x  1,
4.
if 0  x  4
if 0  x  4
if x  1, 2, 3, 4
if x  0, 1, 2, 3
Unit 1.5
1,
2,

C. f ( x)  
3,
4,
if 0  x  1
if 1  x  2
1,
2,

D. f ( x)  
3,
4,
if 0  x  1
if 1  x  2
if 2  x  3
if 3  x  4
if 2  x  3
if 3  x  4
Graph the function:
y
a.
–10 –8
–6
–4
y
c.
10
10
8
8
6
6
4
4
2
2
–2
–2
2
4
6
8
10
x
–10 –8
–6
–4
–2
–2
–4
–4
–6
–6
–8
–8
–10
–10
Alg II Notes Unit 1.5 Piecewise Functions
Page 2 of 5
2
4
6
8
10
x
Algebra II Notes
Piecewise Functions
y
b.
–10 –8
5.
–6
–4
10
8
8
6
6
4
4
2
2
–2
–2
2
4
6
8
10
x
–10 –8
–6
–4
–2
–2
–4
–4
–6
–6
–8
–8
–10
–10
2
4
6
8
10
x
2
4
6
8
10
x
2
4
6
8
10
x
.
y
a.
–6
–4
10
8
8
6
6
4
4
2
2
–2
–2
2
4
6
8
10
x
–4
–10 –8
–6
–4
–2
–2
–4
–4
–6
–6
–8
–8
–10
–10
y
–6
y
c.
10
b.
–10 –8
y
d.
10
Graph
–10 –8
Unit 1.5
y
d.
10
10
8
8
6
6
4
4
2
2
–2
–2
2
4
6
8
10
x
–10 –8
–6
–4
–2
–2
–4
–4
–6
–6
–8
–8
–10
–10
Alg II Notes Unit 1.5 Piecewise Functions
Page 3 of 5
Algebra II Notes
Piecewise Functions
Unit 1.5
6. A shipping company charges $3.50 to ship a package weighing one pound or less. Then they charge
$1.50 for each additional pound, or fraction of a pound, up to five pounds. Write a piecewise
function that gives the price P for shipping a package weighing w pounds. Graph the function.
a.
c.
Priority Mail Rates
10
9
9
8
8
Shipping Cost ($)
Shipping Cost ($)
Priority Mail Rates
10
7
6
5
4
3
7
6
5
4
3
2
2
1
1
1
2
3
4
5
1
Weight (lbs)
2
3
4
5
4
5
Weight (lbs)
b.
d.
Priority Mail Rates
10
9
9
8
8
Shipping Cost ($)
Shipping Cost ($)
Priority Mail Rates
10
7
6
5
4
3
7
6
5
4
3
2
2
1
1
1
2
3
4
5
1
Weight (lbs)
Alg II Notes Unit 1.5 Piecewise Functions
2
3
Weight (lbs)
Page 4 of 5
Algebra II Notes
Piecewise Functions
7. Which graph represents the piecewise function?
3x  1, x  1
f  x  
 x  2, x  1
A.
C.
B.
D.
8. Evaluate f ( 3) for the piecewise function:
 x,
f ( x)   2
 x  3 x,
x0
x0
A. f (3)  18
B. f (3)  3
C. f (3)  0
D. f (3)  18
Alg II Notes Unit 1.5 Piecewise Functions
Page 5 of 5
Unit 1.5