1. MSM07G7_RESBK_Ch04_027-034.pe 1/30/06 9:17 PM Page 30
Name Date Class
LESSON Reteach
4-4 Functions, Tables, and Graphs
A function is a relationship in which the value of one quantity
depends on the value of another quantity. A function can be
represented by a rule or an equation. A function table can
help you find the ordered pair values for a function.
Complete the missing values in the table.
Input Rule Output Ordered Pair
x 3x ؉ 2 y (x, y)
1. ؊2 3(؊2) ؉ 2 ‫2 ؉ 6؊ ؍‬ ؊4 (؊2, ؊4)
2. ؊1 3(؊1) ؉ 2 ‫2 ؉ 3؊ ؍‬ ؊1 (؊1, ؊1)
3. 0 3(0) ؉ 2 ‫2 ؉ 0 ؍‬ 2 (0, 2)
4. 1 3(1) ؉ 2 ‫2 ؉ 3 ؍‬ 5 (1, 5)
y
(1, 5)
You can graph the resulting ordered pairs 4
from the input/output table.
(0, 2)
2
x
؊4 ؊2 O 2 4
(؊1, ؊1)
؊2
(؊2, ؊4)
؊4
Find the output for each input value, and graph the resulting
ordered pairs. y
5. y ‫2 ؍‬x ؊ 1 4
Input Rule Output Ordered Pair
x 2x ؊ 1 y (x, y) 2
؊2 2(؊2) ؊ 1 ؊5 (؊2, ؊5) x
؊1 2(؊1) ؊ 1 ؊3 (؊1, ؊3) ؊4
4 ؊2
2 O 2 4
0 2(0) ؊ 1 ؊1 (0, ؊1) ؊2
1 2(1) ؊ 1 1 (1, 1)
؊4
2 2(2) ؊ 1 3 (2, 3)
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2. MSM07G7_RESBK_Ch04_051-062.pe 1/30/06 9:32 PM Page 57
Practice A
LESSON Practice B
LESSON
4-4 Functions, Tables, and Graphs 4-4 Functions, Tables, and Graphs
Find the output for each input. Find the output for each input.
1. y ‫ ؍‬x ؉ 5 2. y ‫3 ؍‬x 1. y ‫5 ؍‬x ؊ 1 2. y ‫2؊ ؍‬x 2
Input Rule Output Input Rule Output Input Rule Output Input Rule Output
x x؉5 y x 3x y x 5x ؊ 1 y x ؊2x 2 y
0 0؉5 5 0 3(0) 0 ؊2 5(؊2) ؊ 1 ؊11
؊2 ؊2(؊2)2 ؊8
1 1؉5 6 1 3(1) 3 0 5(0) ؊ 1 ؊1
2 2؉5 7 2 3(2) 6 3 5(3) ؊ 1 14 2 ؊2(2)2 ؊8
3. y ‫3 ؍‬x ؊ 4 4. y ‫ ؍‬x 2 6 5(6) ؊ 1 29 3 ؊2(3)2 ؊18
Input Rule Output Input Rule Output 4 ؊2(4)2 ؊32
2
x 3x ؊ 4 y x x y Make a function table, and graph the
0 3(0) ؊ 4 ؊4 0 (0)2 0 resulting ordered pairs.
1 3(1) ؊ 4 ؊1 1 (1)2 1 3. y ‫ ؍‬x ، 4
2 y
2 3(2) ؊ 4 2 2 (2) 4
Input Rule Output Ordered Pair
4
Make a function table. Graph the resulting y x x،4 y (x, y)
2
ordered pairs.
4 ؊4 ؊4 ، 4 ؊1 (؊4, ؊1)
(2, 1 ) (4, 1)
2
5. y ‫2 ؍‬x ؊ 4 (0, 0) x
Ordered 2 0 0،4 0 (0, 0) ؊4 ؊2 O 2 4
Input
x
Rule
2x ؊ 4
Output
y
Pair
(x, y) ؊4 ؊2 O 2
(2, 0)
4
x
2 2،4
1
ᎏᎏ
2 ͑2, ͒1
ᎏᎏ
2
(؊4,؊1) ؊2
؊4
0 2(0) ؊ 41 ؊4 (0, ؊4) ؊2
(1, ؊2) 4 4،4 1 (4, 1)
1 2(1) ؊ 4 1
؊2 (1, ؊2) (0, ؊4)
؊4 4. y ‫ ؍‬x 2 ؊ 5
2 2(2) ؊ 41 0 (2, 0) y
Input Rule Output Ordered Pair 4
2
6. y ‫4 ؍‬x y
x x2 ؊ 5 y (x, y)
Ordered (؊1, 4) 4
(1, 4) 2
Input Rule Output Pair ؊2 (؊2)2 ؊ 5 ؊1 (؊2, ؊1) x
x 4x 2 y (x, y) 2
؊1 4(؊1)2 4 (؊1, 4) ؊1 (؊1)2 ؊ 5 ؊4 (؊1, ؊4) ؊4 ؊2 O 2 4
(0, 0) x (؊2,؊1) ؊2
0 4(0)2 0 (0, 0) ؊4 ؊2 O 2 4 0 (0)2 ؊ 5 ؊5 (0, ؊5)
1 4(1) 2
4 (1, 4) (1,؊4)
؊4
؊2 1 (1)2 ؊ 5 ؊4 (1, ؊4) (؊1,؊4)
(0,؊5)
؊4
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All rights reserved.
27 Holt Mathematics Copyright © by Holt, Rinehart and Winston.
All rights reserved. 28 Holt Mathematics
Practice C
LESSON Reteach
LESSON
4-4 Functions, Tables, and Graphs 4-4 Functions, Tables, and Graphs
Make a function table, and graph the resulting ordered pairs. A function is a relationship in which the value of one quantity
x depends on the value of another quantity. A function can be
1. y ‫ ؍‬ᎏᎏ
3 y represented by a rule or an equation. A function table can
help you find the ordered pair values for a function.
4
Input Rule Output Ordered
Pair
2 Complete the missing values in the table.
x
ᎏᎏ (3, 1)
x y (x, y)
3 (0, 0) x Input Rule Output Ordered Pair
؊3
؊3 ᎏᎏ
3
؊1 (؊3, ؊1) ؊4 ؊2 O 2 4 x 3x ؉ 2 y (x, y)
0
0
ᎏᎏ 0 (0, 0)
(؊3,؊1) ؊2 1. ؊2 3(؊2) ؉ 2 ‫2 ؉ 6؊ ؍‬ ؊4 (؊2, ؊4)
3
2. ؊1 3(؊1) ؉ 2 ‫2 ؉ 3؊ ؍‬ ؊1 (؊1, ؊1)
؊4
3. 0 3(0) ؉ 2 ‫2 ؉ 0 ؍‬ 2 (0, 2)
4. 1 3(1) ؉ 2 ‫2 ؉ 3 ؍‬ 5 (1, 5)
y
(1, 5)
2. y ‫2 ؍‬x 2 ؊ 4 You can graph the resulting ordered pairs 4
y from the input/output table.
(0, 2)
(؊2, 4) 4
(2, 4) 2
Input Rule Output Ordered Pair
x
x 2x 2 ؊ 4 y (x, y) 2
؊4 ؊2 O 2 4
2 (؊1, ؊1)
؊2 2(؊2) ؊ 4 4 (؊2, 4) x ؊2
؊4 ؊2 O
0 2(0)2 ؊ 4 ؊4 (0, ؊4) 2 4
(؊2, ؊4)
؊2 ؊4
1 2(1)2 ؊ 4 ؊2 (1, ؊2) (1,؊2)
2
2 2(2) ؊ 4 4 (2, 4) ؊4
(0,؊4)
Find the output for each input value, and graph the resulting
ordered pairs. y
3. For every dollar you spend at the Input Rule Output 5. y ‫2 ؍‬x ؊ 1 4
Rusty Nail hardware chain, you (2, 3)
receive 20 Gold Hammer points that
x 20x y Input Rule Output Ordered Pair
can be redeemed for free 10 20(10) 200 x 2x ؊ 1 y (x, y) 2
(1, 1)
merchandise. The equation y ‫02 ؍‬x 25 20(25) 500 ؊2 2(؊2) ؊ 1 ؊5 (؊2, ؊5) x
gives the number of points y received
for spending x dollars. Make an
50 20(50) 1,000 ؊1 2(؊1) ؊ 1 ؊3 (؊1, ؊3) ؊4 ؊2 O 2 4
(0,؊1)
input/output table using the values 80 20(80) 1,600 0 2(0) ؊ 1 ؊1 (0, ؊1) ؊2
x ‫.08 ,05 ,52 ,01 ؍‬ 1 2(1) ؊ 1 1 (1, 1) (؊1,؊3)
؊4
2 2(2) ؊ 1 3 (2, 3) (؊2,؊5)
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
29 Holt Mathematics Copyright © by Holt, Rinehart and Winston.
All rights reserved.
30 Holt Mathematics
Copyright © by Holt, Rinehart and Winston.
57 Holt Mathematics