Name ———————————————————————
Date ————————————
Practice A
LESSON
1.6
For use with pages 35241
Complete the sentence. 1. The collection of all output values is called the 2. The collection of all input values is called the
? of a function. ? of a function.
Identify the domain and range of the function. 3.
4.
Input
Output
8
7
3
7
5 7
5.
Input
Output
4
0.4
15
2
2
0.5
13
6
5
1
0.6
11
5
3
5
0.7
9
Input
Output
Input
Output
6
3
10
9
3
1
11
3
0
2
12
6
3
4
13
9
Input
Output
1
LESSON 1.6
6.
Input
Output
3
8
6
3
9
4
12
7
7.
8.
Make a table for the function. Identify the range of the function. 9. y 5 4x
Domain: 0, 1, 2, 3
10. y 5 x 1 2
Domain: 11, 15, 22, 27
11. y 5 x 2 3
Domain: 5, 9, 14, 19
12. Flower Garden You have a flat of 12 plants that you are planting in a garden. a. Copy and complete: Each time you put one plant in the garden, you have one
less plant in the flat, so ? is a function of ? . b. Write a rule for the number of plants y you have left in the flat as a function of the number of plants x you have put in the garden so far. c. Make a table and identify the range of the function. 13. Centerpieces A florist is making centerpieces for a charity event. She is using
9 flowers in each centerpiece. Write a rule for the total number of flowers used as a function of the number of centerpieces created. 14. Kickboxing You join a kickboxing class at a local gym. The cost is $5 per class
plus $25 for the initial membership fee. Write a rule for the total cost of the class in dollars as a function of the number of classes you attend. How much will it cost if you go to 8 classes?
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Algebra 1 Chapter 1 Resource Book
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
Tell whether the pairing is a function.
Name ———————————————————————
Date ————————————
Practice B
LESSON
1.6
For use with pages 35241
Complete the sentence. 1. The input variable is called the
? variable.
2. The output variable is called the
? variable.
Tell whether the pairing is a function. 3.
Input
Output
1 3
4.
Input
Output
15
5
5
20
6
5
5
15
7
5
7
20
8
5
5.
Input
Output
6
4
12
3
12
2
18
1
Make a table for the function. Identify the range of the function. 6. y 5 4x 2 2
1 8. y 5 } x 1 2 2
7. y 5 0.1x 1 3
Domain: 1, 2, 3, 4
Domain: 10, 20, 30, 40
Domain: 6, 7, 8, 9
9.
Input, x
1
2
3
4
Output, y
5
10
15
20
10.
Input, x
10
11
12
13
Output, y
3
4
5
6
11. Shoe Sizes The table shows men’s shoe sizes in the United States and Australia.
Write a rule for the Australian size as a function of the United States’ size. U.S. size
5
6
7
8
9
10
Australian size
3
4
5
6
7
8
LESSON 1.6
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
Write a rule for the function.
12. Balloon Bunches You are making balloon bunches to attach to tables for a charity
event. You plan on using 8 balloons in each bunch. Write a rule for the total number of balloons used as a function of the number of bunches created. Identify the independent and dependent variables. How many balloons will you use if you make 10 bunches? 13. Baking A baker has baked 10 loaves of bread so far today and plans on baking
3 loaves more each hour for the rest of his shift. Write a rule for the total number of loaves baked as a function of the number of hours left in the baker’s shift. Identify the independent and dependent variables. How many loaves will the baker make if he has 4 hours left in his shift?
Algebra 1 Chapter 1 Resource Book
63
Name ———————————————————————
Date ————————————
Practice C
LESSON
1.6
For use with pages 35241
Tell whether the pairing is a function. 1.
Input
Output
0.2
1.5
0.4
2.
1.25
0.6
1.5
0.8
1.25
Input
Output
5.1
4.3
5.2
4.2
5.3
4.1
3.
Input
Output
25
14
30
13
30
12
35
11
5.4
Make a table for the function. Identify the range of the function. 0.1x 1 2 6. y 5 } 3
3 1 5. y 5 } x 1 } 4 4
1 4. y 5 } x 2 4 3
Domain: 12, 15, 18, 21
Domain: 1, 3, 5, 7
Domain: 10, 20, 30, 40
7.
Input, x
0
1
2
3
Output, y
3
5
7
9
8.
Input, x
16
14
12
10
Output, y
7
6
5
4
LESSON 1.6
9. Shoe Sizes The table shows men’s shoe sizes in the United States and Europe. Write
a rule for the European size as a function of the United States’ size. Then use your function to predict the European size of a U.S. size 11 shoe. U.S. size
3.5
4
4.5
5
5.5
6
European size
35
35.5
36
36.5
37
37.5
10. Birthday Party You are making treat bags for a birthday party. You have made 3 bags
so far, placing 6 novelty items (stickers, balloons, whistles, etc.) in each bag. You will continue to make the bags using 6 items in each bag. Write a rule for the total number of items used as a function of the number of bags created in addition to the first three. How many novelty items will you use if you make 9 more bags? 11. Sandwich Rings A delicatessen worker has created 8 large sandwich rings in the
first 2 hours of her shift. She plans on making sandwich rings at the same rate for the rest of her shift. Write a rule for the total number of sandwich rings made as a function of the number of hours left in the deli worker’s shift. How many sandwich rings will the deli worker make if she has 6 hours left in her shift?
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Algebra 1 Chapter 1 Resource Book
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
Write a rule for the function.
Name ——————————————————————— LESSON
1.6
Date ————————————
Challenge Practice For use with pages 35–41
1. Make a table for the function y 5 3x2 1 2. Determine the domain values corre-
sponding to range values of 2, 5, 14, and 29. 2. Make a table for the function y 5 2x3 1 1. Determine the domain values corre-
sponding to range values of 3, 17, 55, and 251. 3. The function y 5 x2 1 1 has the following table associated with it.
Input, x Output, y
22
21
0
1
2
3
5
2
1
2
5
10
Suppose the function is reversed, making y the input and x the output. You would have to remove some of the values of y from the table in order to have x be a function of y. What would be the minimum number of y-values you would have to remove from the table in order to have x be a function of y? 4. Refer to Exercise 3. What y-values would you have to remove from the table? 5. Consider the table for a function.
Input, x Output, y
22
21
n
1
2
3
3
4
4
6
5
10
LESSON 1.6
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
For what value of n would this table represent x as a function of y?
Algebra 1 Chapter 1 Resource Book
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Name ——————————————————————— LESSON
1.6
Date ————————————
Interdisciplinary Application For use with pages 35–37
Paul Revere History Paul Revere, made famous by Henry Wadsworth Longfellow’s poem, “The Midnight Ride of Paul Revere,” was a major contributor to the Revolutionary War. The famous ride took place on April, 18, 1775. England’s best troops were waiting at the foot of Boston Common to take a boat trip across Back Bay. British Governor General Gage was hoping to seize the gunpowder that the patriots were storing in Concord and keep the patriots from getting support from the other New England colonies. Dr. Joseph Warren sent both Revere and William Dawes from Boston to Lexington to spread the message and warn the assumed targets, John Hancock and Samuel Adams, who were preparing to depart for the meeting of the Second Continental Congress. On the way to Lexington, Dawes had been able to talk his way past the guards along Boston Neck, while Revere stayed downstream from the sailors guarding the Ferryway. Because of some miscommunication by the British after their boat trip, the troops were not reassembled and ready to march through Lexington to Concord until around 1:30 A.M., by which time the Lexington militia had already been assembled.
Imagine that Revere had to travel 1.5 miles to Charleston. From Charlestown to Lexington he was able to ride a horse that traveled at a rate of 1214 feet per minute for 35 minutes. Represent his total distance traveled D as a function of the time t (in minutes) that Revere traveled by horse. (Hint: Be sure to include the initial 1.5 miles in the equation and to convert to feet (1 mile 5 5280 feet).) 1. Write an equation for the function, applying the problem-solving strategies you
learned in Lesson 1.5. (Write a verbal model and assign labels first.) 2. Use your equation to make an input-output table for the function. For inputs, use the
time increment of 5 minutes until you reach 35 minutes. 3. About how many total miles did Revere travel to reach Lexington that night? Write
your answer to the nearest tenth of a mile. 4. Imagine that Revere had to walk the entire distance that night. If he could walk
at a rate of 440 feet per minute, how long would it take him to reach Lexington? The distance Revere traveled D is modeled by D 5 440t where t represents the time in minutes. Make an input-output table for the function. For inputs, use time increment of 10 minutes. (Hint: Use your answer from Exercise 3 converted to feet to find Revere’s total distance traveled.
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Algebra 1 Chapter 1 Resource Book
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
LESSON 1.6
When Revere and Dawes resumed their ride to Concord, they (along with Dr. Samuel Prescott) were stopped by a patrol of British soldiers. Dawes and Prescott were able to get away to continue their warning, while Revere was held at gunpoint and his horse taken. Revere was able to deceive the officers with tales of great patriot resistance, so fearing their own lives they allowed him to leave. Revere returned to Hancock and Adams with a new message that the British would be attempting to get the gunpowder at Concord. General Gage’s plan to squash the planned rebellion backfired and the American Revolutionary War had begun.
Name ——————————————————————— LESSON
1.6
Date ————————————
Study Guide For use with pages 35241 GOAL
Represent functions as rules and as tables.
Vocabulary A function consists of: • A set called the domain containing numbers called inputs, and a set called the range containing numbers called outputs. • A pairing of inputs with outputs such that each input is paired with exactly one output. The input variable is called an independent variable. The output variable is called the dependent variable because its value depends on the value of the input variable.
EXAMPLE 1
Identify the domain and range of a function The input-output table shows the price of various lobsters at a fish market. Identify the domain and range of the function. Input (pounds)
2.3
3.1
4.2
$7.80
$11.96
$16.12
$21.82
Solution
The domain is the set of inputs: 1.5, 2.3, 3.1, and 4.2.
LESSON 1.6
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
Output (dollars)
1.5
The range is the set of outputs: 7.80, 11.96, 16.12, and 21.82.
Exercises for Example 1 Identify the domain and range of the function. 1.
2.
Input
2
5
7
8
Output
5
11
15
17
Input
1
3
4
7
Output
2
8
11
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Algebra 1 Chapter 1 Resource Book
65
Name ——————————————————————— LESSON
1.6
Study Guide
Date ————————————
continued
For use with pages 35241
EXAMPLE 2
Make a table for a function The domain of the function y 5 x 2 3 is 2, 5, 8, and 11. Make a table for the function, then identify the range of the function. Solution
2
5
8
11
2 2 3 5 21
52352
82355
11 2 3 5 8
x y5x23
The range of the function is 21, 2, 5, and 8.
Exercises for Example 2 Make a table for the function. Identify the range of the function. 3. y 5 4x
Domain: 0, 3, 5, and 7 4. y 5 3x 2 2
Domain: 1, 2, 3, and 4
Write a function rule
LESSON 1.6
Write a rule for the function. Input
3
6
7
10
Output
15
30
35
50
Solution
Let x be the input, or independent variable, and let y be the output, or dependent variable. Notice that each output is 5 times the corresponding input. So, a rule for the function is y 5 5x.
Exercises for Example 3 Write a rule for the function. 5.
6.
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Algebra 1 Chapter 1 Resource Book
Input
3
5
7
9
Output
14
16
18
20
Input
6
7
8
9
Output
3
3.5
4
4.5
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
EXAMPLE 3
