Name
LESSON
9-2
Date
Class
Reteach
Piecewise Functions
A piecewise function has different rules for different parts of its domain.
To evaluate a piecewise function for a given value of x, find the interval that x belongs to.
Then find the corresponding definition of the function for that interval.
When x ⱕ ⫺1, f x ⫽ ⫺6.
f x ⫽
{
⫺6 if x ⱕ ⫺1
2 if ⫺1 ⬍ x ⬍ 4
10 if x ⱖ 4
When ⫺1 ⬍ x ⬍ 4, f x ⫽ 2.
When x ⱖ 4, f x ⫽ 10.
At x ⫽ ⫺5,
x lies in the interval
x ⱕ ⫺1, since ⫺5 ⬍ ⫺1.
At x ⫽ 0,
x lies in the interval
⫺1 ⬍ x ⬍ 4, since
⫺1 ⬍ 0 ⬍ 4.
At x ⫽ 5,
x lies in the interval
x ⱖ 4, since 5 ⬎ 4.
So, f ⫺5 ⫽ ⫺6.
So, f 0 ⫽ 2.
So, f 5 ⫽ 10.
g x ⫽ 4x2 ⫺ 1 if x ⬍ 2
x ⫹ 3 if x ⱖ 2
{
When x ⬍ 2, g x ⫽ 4x ⫺ 1.
When x ⱖ 2, g x ⫽ x 2 ⫹ 3.
At x ⫽ ⫺5, x lies in the interval
x ⬍ 2, since ⫺5 ⬍ 2.
At x ⫽ 5, x lies in the interval
x ⱖ 2, since 5 ⬎ 2.
Use g x ⫽ 4x ⫺ 1 to evaluate g ⫺5 .
2
Use g x ⫽ x ⫹ 3 to evaluate g 5 .
g ⫺5 ⫽ 4 ⫺5 ⫺ 1 ⫽ ⫺21
2
g 5 ⫽ 5 ⫹ 3 ⫽ 28
Evaluate each piecewise function for x 2 and x 4.
0 if x ⱕ ⫺3
1. h x ⫽ 2 if ⫺3 ⬍ x ⱕ 1
6 if x ⬎ 1
{
2
h ⫺2 ⫽
h 4 ⫽
6
2. k x ⫽ 2x ⫺ 1 if x ⱕ ⫺1
3x ⫹ 2 if x ⬎ ⫺1
2
{
k ⫺2 ⫽ 2 2
2
⫺1
3. p x ⫽ 2x2 ⫹ 5 if x ⬍ 0
x ⫺ 5 if x ⱖ 0
{
p 2 1
p 4 11
7
k 4 ⫽ 3 4
⫹2
14
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
a207c09-2_rt.indd 14
14
Holt Algebra 2
1/4/06 7:04:44 PM
Process Black
Name
LESSON
9-2
Date
Class
Reteach
Piecewise Functions (continued)
Use a table of values to graph a piecewise function.
Graph: f x ⫽ 2x ⫹ 4 if x ⬍ ⫺1
⫺x ⫹ 3 if x ⱖ ⫺1
{
Evaluate both 2x ⫹ 4 and
⫺x ⫹ 3 at x ⫽ ⫺1 to graph.
Make a table of values.
x
f x 2x 4
f x x 3
⫺4
2 ⫺4 ⫹ 4 ⫽ ⫺4
⫺3
2 ⫺3 ⫹ 4 ⫽ ⫺2
⫺2
2 ⫺2 ⫹ 4 ⫽ 0
⫺1
2 ⫺1 ⫹ 4 ⫽ 2
⫺ ⫺1 ⫹ 3 ⫽ 4
0
⫺ 0 ⫹ 3 ⫽ 3
1
⫺ 1 ⫹ 3 ⫽ 2
2
⫺ 2 ⫹ 3 ⫽ 1
Y
X
Check the split.
At x ⫽ ⫺1, f x ⫽ ⫺x ⫹ 3.
Put a closed circle at ⫺1, 4 .
Put an open circle at ⫺1, 2 .
Complete the table and graph the function.
4. g x ⫽ ⫺2x if x ⱕ 1
x ⫺ 4 if x ⬎ 1
{
Put a closed circle at
x
g x 2x
⫺2
2 2 4
2 1 2
2 0 0
2 1 2
⫺1
0
1
2
3
4
1, 2 .
1, 3 Put an open circle at
g x x 4
.
Y
1 4 3
2 4 2
3 4 1
440
X
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
a207c09-2_rt.indd 15
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