The document is a lesson on functions from a mathematics textbook. It contains two examples of function tables with missing values that students are asked to complete based on the given rules. It also contains two practice problems asking students to make function tables for additional functions based on given rules and input/output pairs. The tables are used to represent relationships between input and output values defined by functions, which can then be graphed on a coordinate plane from the ordered pairs.

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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All rights reserved. 30 Holt Mathematics

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
Copyright © by Holt, Rinehart and Winston.
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