Reteach function tables

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) Copyright © by Holt, Rinehart and Winston. All rights reserved. 30 Holt Mathematics

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

Reteach function tables

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