Lesson 2.1 Skills Practice Name_________________________________________________________ Date__________________________
Patterns, Patterns, Patterns . . . Developing Sequences of Numbers from Diagrams and Contexts
Vocabulary Define each term in your own words. 1. sequence
2. term
3. ellipsis
Problem Set Write or draw the term requested for each given sequence. 1. 3, 6, 9, 12, 15, …
2. Z, Y, X, W, V, U, …
What is the next term?
What is the tenth term?
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18 3. i, ii, iii, iiii, iiiii, …
4. What is the eighth term?
What is the twentieth term?
,
,
,
,
,...
Chapter 2 Skills Practice • 355
Lesson 2.1 Skills Practice
5. I, II, III, IV, V, VI, …
page 2
6.
What is the eleventh term?
What is the sixth term?
Draw a picture and use a sequence to solve each problem. 7. Marta is decorating the rectangular top of a jewelry box with antique buttons that are all the same size. She has started by gluing 8 buttons across and 5 buttons down for a total of 13 buttons. Write a sequence of numbers to represent the number of buttons used for each group of buttons across and down that she uses to cover the box. How many total buttons will she need?
8. The cheerleaders wanted to create a pyramid for the halftime show. There are 6 members of the team who are strong enough to be at the bottom of the pyramid. Use a sequence to determine how many cheerleaders can participate in the pyramid.
356 • Chapter 2 Skills Practice
© 2011 Carnegie Learning
13, 11, 9, 7, 5, 3. Marta will need 48 buttons.
Lesson 2.1 Skills Practice
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Name_________________________________________________________ Date__________________________ 9. A banquet hall has hexagonal tables. One person can be seated at each side. The diagram shows how the tables are placed together for large parties. Write a sequence to determine the number of people that can be seated around one, two, three, four, five, six, seven, and eight tables. O
O
O
O O
O
10. Kim has small wooden cube-shaped blocks. To make the next size cube using the blocks, she needs 8 blocks. Write a sequence to show the number of blocks needed for each increasingly
© 2011 Carnegie Learning
larger cube that can be made. Include at least 6 terms in the sequence.
11. Clayton is making a trestle bridge for his miniature train display. The rods he is using are shaped to create a triangle when fitted together. He starts with 3 rods, making 1 triangle. To finish 1 side of the trestle, he needs 11 triangles. Write a sequence to determine the number of rods Clayton needs to make both sides of the trestle bridge.
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Lesson 2.1 Skills Practice
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12. Keisha is slicing a large pizza into 32 equal slices. The pizza is already cut in half. She starts with 1 cut making 4 slices. She doubles the number of cuts she makes each time after that. Write a sequence showing the number of cuts she makes and another sequence showing the number of slices she creates. How many cuts should Keisha make to get 32 slices?
Write a sequence to solve each problem. 13. Peter’s aquarium is too heavy to lift when it is filled with water. He needs to bail out at least half of the water and replace it with fresh water. The aquarium holds 10 gallons and the container he uses to bail water holds 3 pints. Write a sequence to show how the water decreases with each bailing and determine how many times he must bail with the pint container to remove at least half of the water in the aquarium. (Hint: There are 8 pints in 1 gallon.)
80, 77, 74, 71, 68, 65, 62, 59, 56, 53, 50, 47, 44, 41, 38 Peter must bail 14 times to remove at least half of the water.
358 • Chapter 2 Skills Practice
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10 gal 3 8 pt/gal 5 80 pt
Lesson 2.1 Skills Practice
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Name_________________________________________________________ Date__________________________ 14. A runner starts running a race as fast as he can, but he gradually runs out of energy and slows down along the way. He starts running at a pace of 6 minutes per mile. After every 2 miles, he slows down by 1 minute per mile. Write a sequence to show how many minutes it will take him to run 12 miles.
15. Tanya dropped her lucky penny from a hot air balloon at about 700 feet. The penny fell 32 feet per second until it hit the ground. Write a sequence to show the height of the penny each second as it fell and determine about how many seconds it took for the penny to hit the ground.
16. Samuel earns $30 per week for mowing grass on Mondays. He also spends $8 per week on comic
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books each Saturday. Samuel checks his account balance each Sunday and Wednesday. Starting at $0 on the first Sunday, write a sequence showing the amount of money Samuel has each time he checks his account balance. Assuming he does not spend his money on anything other than comic books, how long will it take Samuel to save enough money to buy a $200 bike?
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17. The eighth grade is collecting books for a used-book sale. On the first day of collections, they received 20 books. Each day after that they received the amount they received the previous day plus 5 books. Write a sequence to show the number of books collected each day and the total number of books collected after 2 weeks (school days only).
18. Scientists determined that the population of an endangered species was decreasing by one half each year. At the start of a 7-year study, the species had a population of 8000. Write a sequence
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that shows the population at the start of each year during the study.
360 • Chapter 2 Skills Practice
Lesson 2.2 Skills Practice Name_________________________________________________________ Date__________________________
Every Graph Tells a Story Describing Characteristics of Graphs
Vocabulary Explain the difference between the set of terms. 1. Explain the difference between a graph that is discrete and a graph that is continuous.
2. Explain the difference between a graph that is linear and a graph that is nonlinear.
Problem Set Tell whether each graph is discrete or continuous. Also, tell whether each graph is increasing, decreasing, both, or neither.
© 2011 Carnegie Learning
1.
2.
y
y
10
10
9
9
8
8
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7
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10
x
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x
The graph is discrete and decreasing.
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4.
y
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6.
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362 • Chapter 2 Skills Practice
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y
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1
1
x
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3.
page 2
Lesson 2.2 Skills Practice
page 3
Name_________________________________________________________ Date__________________________ Tell whether each graph is linear or nonlinear. Also, tell whether each graph is increasing, decreasing, both, or neither. 7.
8.
y
y
10
10
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1 1
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3
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10
x
1
2
3
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5
6
7
8
9
10
1
2
3
4
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6
7
8
9
10
x
The graph is linear and neither increasing nor decreasing.
© 2011 Carnegie Learning
9.
10.
y
y
10
10
9
9
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x
Chapter 2 Skills Practice • 363
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11.
page 4
y 10 9 8 7 6 5 4 3 2 1
12.
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y 10 9 8 7 6 5 4 3 2 1
364 • Chapter 2 Skills Practice
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x
Lesson 2.2 Skills Practice
page 5
Name_________________________________________________________ Date__________________________ Tell a story to describe each graph. 13.
The plant starts with many leaves and
y
loses a few and then loses a lot in a short amount of time. Then, the plant starts Number of leaves on plant
slowly gaining leaves. Perhaps the plant was not watered during the time when a large number of leaves were dropping off. Finally, the plant was watered and started to grow again.
x
© 2011 Carnegie Learning
Day
Chapter 2 Skills Practice • 365
Lesson 2.2 Skills Practice
14.
page 6
Height of rocket
y
x Second
15.
x Day
366 • Chapter 2 Skills Practice
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Heating oil used
y
Lesson 2.2 Skills Practice
page 7
Name_________________________________________________________ Date__________________________ 16.
Jason’s savings account balance
y
x Month
17.
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Distance Dan ran
y
x Day
Chapter 2 Skills Practice • 367
Lesson 2.2 Skills Practice
18.
page 8
Weight of a puppy
y
x
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Month
368 • Chapter 2 Skills Practice
Lesson 2.3 Skills Practice Name_________________________________________________________ Date__________________________
To Be or Not To Be a Function? Defining and Recognizing Functions
Vocabulary Write the term from the box that best completes each sentence. scatter plot output relation input vertical line test mapping set domain range function
1. A(n)
is any set of ordered pairs or the mapping between a set of inputs and a
set of outputs. 2. The first coordinate of an ordered pair in a relation is the
.
3. The second coordinate of an ordered pair is the
.
4. A(n)
maps each input to one and only one output.
5. A(n)
is a graph of a collection of ordered pairs.
6. The
is a visual method of determining whether a relation represented as a
graph is a function by visualizing whether any vertical lines would intersect the graph of the relation at more than one point or not. 7. A(n)
shows objects in two sets connected together to represent a relationship
between the two sets.
© 2011 Carnegie Learning
8. A(n)
is a collection of numbers, geometric figures, letters, or other objects that
have some characteristic in common. 9. The
of a function is the set of all inputs of the function.
10. The
of a function is the set of all outputs of the function.
Chapter 2 Skills Practice • 369
Lesson 2.3 Skills Practice
page 2
Problem Set Write the corresponding ordered pairs and tell whether each relation is a function. 1.
2. 1 2 3 4
4 6 8 10
1 2 3 4
3 4 5 6
(1, 4), (2, 6), (3, 8), (4, 10) The relation is a function.
5
6
10
7
20
8
30
10
370 • Chapter 2 Skills Practice
Input
Output
4
8
8
12
12
16
16
20
20
24
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4.
3.
Lesson 2.3 Skills Practice
page 3
Name_________________________________________________________ Date__________________________ 5.
6.
Input
Output
x
y
15
0
0
15
10
5
5
10
5
10
10
5
10
15
15
10
15
20
20
15
Determine whether each graph represents a function. Use the vertical line test, if necessary.
© 2011 Carnegie Learning
7.
8.
y
y
10
10
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1 1
2
3
4
5
6
7
8
9
10
x
1
2
3
4
5
6
7
8
9
10
x
The scatter plot is not a function. A vertical line can be drawn through (4, 1) and (4, 5).
Chapter 2 Skills Practice • 371
Lesson 2.3 Skills Practice
10.
y
y
10
10
9
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1 1
11.
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12.
y
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372 • Chapter 2 Skills Practice
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9.
page 4
Lesson 2.3 Skills Practice
page 5
Name_________________________________________________________ Date__________________________ Determine whether each equation is a function. If it is not a function, explain why not. 13. y 5 3x 1 1
14. y 5 x2
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The equation is a function.
______
15. y2 5 x
16. y 5 √ x 1 5
17. y 5 2|x|
18. √y 5 x 2 8
1 x 19. y 5 __ 2
20. | y| 5 6 1 4x
__
Determine whether each given situation represents a function. Explain your answer. 21. Input: Lila mails 6 different valentines to her friends.
Output: Each of Lila’s 6 friends receives a valentine from her. Yes. Each friend receives just 1 valentine from Lila.
Chapter 2 Skills Practice • 373
Lesson 2.3 Skills Practice
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22. Input: There is 1 copy of a popular book in the library.
Output: The book has been checked out by 45 different people.
23. Input: The principal of a school sends the same memo to all of the teachers.
Output: There are 28 teachers in the school.
24. Input: There are 13 cats for adoption at the animal shelter.
Output: Each cat is adopted by a different family.
25. Input: There are 3 showings of a play.
Output: Over 200 people attend each showing.
26. Input: Garrett bakes 2 dozen cookies for the bake sale. Output: Twenty-four people buy a cookie.
27. Input: The new issue of Sports Today is published.
Output: Issues are sent to millions of readers.
28. Input: Yi Ling has French on Mondays, Wednesdays, and Fridays, and German on Tuesdays and Thursdays.
Output: Yi Ling’s language classes per day.
374 • Chapter 2 Skills Practice
© 2011 Carnegie Learning
Lesson 2.4 Skills Practice Name_________________________________________________________ Date__________________________
Scaling a Cliff Linear Functions
Vocabulary Define the term in your own words. 1. linear function
Problem Set Identify the dependent quantity and the independent quantity in each problem situation. 1. Terrence is purchasing canned vegetables at his local grocery store to donate to the local food pantry. Each can costs $0.39. The total amount of money spent on the canned vegetables is the dependent quantity. The number of cans he purchases is the independent quantity.
© 2011 Carnegie Learning
2. Rosita’s pet rabbits eat 12 ounces of rabbit food every day.
3. The amount of electricity used by a light changes as the knob on the dimmer switch is turned.
Chapter 2 Skills Practice • 375
Lesson 2.4 Skills Practice
page 2
4. Stephanie is selling Girl Scout cookies to raise money for her local troop. For each box of cookies she sells, the troop receives $2.00.
5. The height reached by a water-propelled rocket is directly related to the amount of water pressure within the rocket.
6. As an engineer opens the release gate on a dam’s spillway, the amount of water released from the
© 2011 Carnegie Learning
lake increases.
376 • Chapter 2 Skills Practice
Lesson 2.4 Skills Practice
page 3
Name_________________________________________________________ Date__________________________ Complete the table and create a graph for each given problem situation. In the “Expression” row of the table, write a variable to represent the independent quantity in the first column and write an expression to represent the dependent quantity in terms of the independent quantity in the second column. 7. The Rivue Restaurant on the 25th floor of the Galt House in Louisville, Kentucky rotates 2.5 times every hour. Independent Quantity
Dependent Quantity
Quantity Name
Time
Number of Rotations
Unit of Measure
Hours
Rotations
1
2.5
2
5
4
10
6
15
10
25
t
2.5t
Expression 30
24 21 Number of Rotations
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27
18 15 12 9 6 3 0 0
1
2
3
4
5
6
7
8
9
10
Time (hours)
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Lesson 2.4 Skills Practice
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8. Horace begins measuring the diameter of a pumpkin in his pumpkin patch when it has a diameter of 6 inches. After he measures the pumpkin, its diameter begins to increase at a rate of 2 inches per week.
Independent Quantity
Dependent Quantity
0
6
Quantity Name Unit of Measure
1 12 5 26 Expression
30 27 24 21
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18 15 12 9 6 3 0 0
378 • Chapter 2 Skills Practice
1
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Lesson 2.4 Skills Practice
page 5
Name_________________________________________________________ Date__________________________ 9. Gretchen is filling a water trough for her cows. The water trough has 10 centimeters of water in it when she begins filling it and the water level increases by 5 centimeters every minute. Independent Quantity
Dependent Quantity
Quantity Name Unit of Measure 1 4 50 12 85 Expression
100 90 80
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70 60 50 40 30 20 10 0 0
2
4
6
8
10
12
14
16
18
20
Chapter 2 Skills Practice • 379
Lesson 2.4 Skills Practice
page 6
10. Carl initially had $200 in his savings account. Each week he withdraws $15. Independent Quantity
Dependent Quantity
Quantity Name Unit of Measure 1 155 125 8 50 Expression
200 180 160 140 120
80 60 40 20 0 0
380 • Chapter 2 Skills Practice
2
4
6
8
10
12
14
16
18
20
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100
Lesson 2.4 Skills Practice
page 7
Name_________________________________________________________ Date__________________________ 11. A washing machine rotates at a rate of 6 rotations per second during the spin cycle. Independent Quantity
Dependent Quantity
Quantity Name Unit of Measure 1 30 72 30 300 Expression
300 270 240 210
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180 150 120 90 60 30 0 0
5
10
15
20
25
30
35
40
45
50
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Lesson 2.4 Skills Practice
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12. A corn mill produces 1 ounce of cornmeal with every 4 rotations of the stone-grinding wheel. Independent Quantity
Dependent Quantity
Quantity Name Unit of Measure 4 3 5 36 10 Expression
10 9 8 7 6
4 3 2 1 0 0
382 • Chapter 2 Skills Practice
4
8
12
16
20
24
28
32
36
40
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5
Lesson 2.4 Skills Practice
page 9
Name_________________________________________________________ Date__________________________ 13. A concrete truck has an initial load of 70 cubic yards of concrete. The truck pours concrete at a rate of 0.2 cubic yard per second. Independent Quantity
Dependent Quantity
Quantity Name
Unit of Measure 10 66 50 50 30 Expression
100 90 80
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70 60 50 40 30 20 10 0 0
20
40
60
80
100 120 140 160 180 200
Chapter 2 Skills Practice • 383
Lesson 2.4 Skills Practice
page 10
14. A steamroller travels at a constant rate of 3.5 feet per second. Independent Quantity
Dependent Quantity
Quantity Name Unit of Measure 5 35 25 175 350 Expression
350 315 280 245 210 175
105 70 35 0 0
384 • Chapter 2 Skills Practice
10
20
30
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50
60
70
80
90
100
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140
Lesson 2.5 Skills Practice Name_________________________________________________________ Date__________________________
U.S. Shirts Using Tables, Graphs, and Equations, Part 1
Problem Set Complete the table of values to model each problem situation. 1. You pay $5 to enter a raffle, plus $1 for each raffle ticket. Number of Raffle Tickets Purchased
Total Cost (in dollars)
10
5 1 1(10) 5 15
11
5 1 1(11) 5 16
12
5 1 1(12) 5 17
13
5 1 1(13) 5 18
14
5 1 1(14) 5 19
15
5 1 1(15) 5 20
© 2011 Carnegie Learning
2. A company pays $500 for each computer, plus an $80 shipping charge. Number of Computers in Each Order
Total Cost (in dollars)
5 6 7 8 9 10
Chapter 2 Skills Practice • 385
Lesson 2.5 Skills Practice
page 2
3. Lauren has already read 55 pages of a novel. Each day, she reads another 30 pages. Number of Days
Number of Pages Read
2 4 6 8 10 12
4. Mr. Cloud is writing an autobiography. He has already written 32 pages. Each day, he writes another 5 pages. Number of Days
Number of Pages Written
10 15 20
30 35
386 • Chapter 2 Skills Practice
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25
Lesson 2.5 Skills Practice
page 3
Name_________________________________________________________ Date__________________________ Create a graph of the data in each given table. 5. A video game store sells each game for $30. The store’s total fixed expenses are $500 each month. They record the number of games sold, g, and their total profit, p, in the table below. p
Number of Games Sold
Total Profit (in dollars)
20
100
30
400
1800
Total Profit (in dollars)
1600
40
700
50
1000
60
1300
70
2000
1600
(70, 1600)
1400 (60, 1300)
1200 1000
(50, 1000)
800 (40, 700)
600 400
(30, 400)
200 (20, 100) 10
20
30
40
50
60
70
80
90 100
g
Number of Games Sold
6. A paper store sells each ream of paper for $40. They will deliver it for a one-time fee of $25.
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An office records their total paper costs, c, in dollars, and the total number of reams delivered, r.
Number of Reams Delivered
Total Paper Costs (in dollars)
6
265
8
345
10
425
12
505
14
585
16
665
Chapter 2 Skills Practice • 387
Lesson 2.5 Skills Practice
page 4
7. An architect is designing a new hotel. He is planning to have 10 windows in the lobby, and each hotel room will have 2 windows. The hotel will not have any other windows. He records the total number of windows, w, for different numbers of hotel rooms, r. Number of Hotel Rooms
Total Number of Windows
50
110
75
160
100
210
125
260
150
310
175
360
8. A bookstore spends $300 on a new shipment of 200 books. They sell each book for $12.
Number of Books Sold
Total Profit (in dollars)
40
180
60
420
80
660
100
900
120
1140
140
1380
388 • Chapter 2 Skills Practice
© 2011 Carnegie Learning
They record their total profit, p, in dollars, after selling b books.
Lesson 2.5 Skills Practice
page 5
Name_________________________________________________________ Date__________________________ Use the given information to answer each question. 9. As part of her workout, Dana stretches for 15 minutes before running. She then runs 1 mile in 10 minutes. What is the total time of her workout, including stretching, if Dana runs 5 miles? 15 1 5(10) 5 15 1 50 5 65 Dana’s total workout time is 65 minutes if she runs 5 miles.
10. Evan borrows $200 from his parents. He agrees to pay his parents back an extra dollar for each day that he owes them money. If he waits 90 days to pay back his parents, what is the total amount Evan owes them?
11. A wholesale food store charges a yearly membership of $50. A café owner uses his membership to purchase cases of bottled water. Each case of bottled water costs $5. In 1 year, the café owner buys 200 cases of bottled water. Including the yearly membership, what is the café owner’s total
© 2011 Carnegie Learning
yearly cost, in dollars, for the 200 cases of water?
12. A magazine publisher charges a supermarket $2 for each magazine that the market orders, plus a monthly rental fee of $30 for a magazine rack. If the supermarket orders 350 magazines per month, what is their total cost, in dollars, for the 350 magazines?
Chapter 2 Skills Practice • 389
Lesson 2.5 Skills Practice
page 6
Use the given information to answer each question. 13. Leah is ordering new beach towels. She will pay a $5 fixed shipping charge and $10 for each beach towel. If Leah has $55 dollars to spend on her beach towel order, how many beach towels can she buy?
50 5 5 _______ ___ 5 55 2 5 10
10
With $55, Leah can order 5 new beach towels.
14. Twelve people have a cold. Each day, 8 more people get sick. After how many days will 101 total people be sick?
15. Jackson is ordering pizza for a party. He wants to order 4 pieces for himself, and 3 pieces for every person attending the party. If he orders a total of 34 slices of pizza, how many people are attending
16. Sean is adding to his art collection. He already owns 7 paintings. Each time he visits an art gallery, he buys 2 more paintings. How many galleries will he need to visit if he wants to own at least 20 paintings?
390 • Chapter 2 Skills Practice
© 2011 Carnegie Learning
the party?
Lesson 2.5 Skills Practice
page 7
Name_________________________________________________________ Date__________________________ Write an equation in two variables to model each given situation. 17. A person’s nails grow at an average rate of 1 millimeter per week. You measure one of your nails to be 10 millimeters long. Write an equation that relates ℓ, the total length of your nail, to t, the time in weeks. ℓ 5 t 1 10
18. Devin earns $500 each week, plus $15 for each hour of overtime. Write an equation to represent Devin’s total weekly salary, s, if he works t hours of overtime.
19. A manager is hired at a starting salary of $60,000 per year. Each year, her salary increases by $5000. Write an equation to represent her yearly salary, s, at any given time t, in years.
20. A hair stylist earns $70 per day, plus $20 for each haircut. Write an equation that relates his total
© 2011 Carnegie Learning
daily income d, in dollars, for any number of haircuts, h.
21. A clothing company charges $5 for each belt that it sells. It also charges a fixed delivery fee of $8 per order. Write an equation that relates the total charge c, in dollars, for an order of b belts.
22. A dry cleaner charges $2 to dry clean a shirt, and $10 to dry clean a jacket. Write an equation that relates the total dry cleaning bill b, in dollars, for s shirts and one jacket.
Chapter 2 Skills Practice • 391
© 2011 Carnegie Learning
392 • Chapter 2 Skills Practice
Lesson 2.6 Skills Practice Name_________________________________________________________ Date__________________________
Hot Shirts Using Tables, Graphs, and Equations, Part 2
Vocabulary Define each term in your own words. 1. point of intersection
2. estimation
Problem Set Estimate each value of each expression. Then, calculate the exact value. 1. 750.25 1 225.50
2. 1.98 1 1.73
© 2011 Carnegie Learning
975; 975.75
3. 25 3 101
4. 236 3 4
5. 146.9 2 92.5
6. 4261 2 2637
Chapter 2 Skills Practice • 393
Lesson 2.6 Skills Practice
page 2
Use the given information to complete each table and answer the question. 7. Job A will pay a $30,000 salary per year for the first year, with a $1200 raise each year. Job B will pay a $30,000 salary per year for the first year, with a 3% raise each year. Complete the table to show the annual salaries for the first 4 years, rounding each salary to the nearest dollar. In the fourth year, which job will pay the greater salary?
Year
Job A
Job B
1
$30,000
$30,000
2
$30,000 1 $1200 5 $31,200
$30,000 3 1.03 5 $30,900
3
$31,200 1 $1200 5 $32,400
$30,900 3 1.03 5 $31,827
4
$32,400 1 $1200 5 $33,600
$31,827 3 1.03 5 $32,782
Job A will pay a greater salary. 8. Job C is offering you a $40,000 salary for the first year, plus a one-time $3000 signing bonus. Each year, you get a $1500 raise. Job D is offering you $40,000 for the first year, and each year you get a 5% raise. Complete the table to show the annual salaries for the first 4 years. Which job will pay you more in total for all 4 years?
Year
Job C
Job D
2 3 4
394 • Chapter 2 Skills Practice
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Lesson 2.6 Skills Practice
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Name_________________________________________________________ Date__________________________ 9. You have a choice between two different investment options. You will invest $6000. Investment Plan A estimates that you will earn 6% of your account balance each year. Investment Plan B estimates that you will earn $370 each year. Complete the table to show the account balance for the first 4 years. After 4 years, which investment plan would have a greater account balance?
Year
Plan A
Plan B
1 2 3 4
10. You invest $5000 into each of two different accounts. In Account A, you will earn $50 each month. In Account B, you will earn 1% of your account balance at the end of each month. Complete the table to show the account balance for the first 4 months. After 4 months, which investment plan would have a greater account balance?
Month
Account A
Account B
© 2011 Carnegie Learning
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11. On Big Country Dairy Farms, the average Holstein cow produces 40 pounds of milk daily in its first year of production and an additional 3 pounds of milk daily in each year after the first. The average Jersey cow produces 35 pounds of milk daily in its first year of production and an additional 4.5 pounds of milk daily in each year after the first. Complete the table to show each type of cows’ daily milk production for the first 5 years. After 5 years, which type of cow produces the most milk daily?
Year
Holstein’s Daily Milk Production (pounds)
Jersey’s Daily Milk Production (pounds)
1 2 3 4 5
12. Jerry puts a different type of fertilizer on each of his two pumpkin patches. A pumpkin from Patch A measures 13 ounces in week 1 and grows at a rate of 3.2 ounces per week. A pumpkin from Patch B measures 9 ounces in week 1 and grows at a rate of 3.6 ounces per week. Complete the table to show the growth for each pumpkin for 5 weeks. After 5 weeks, which pumpkin is the largest? Weight of the Patch A Pumpkin (ounces)
1 2 3 4
5
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Weight of the Patch B Pumpkin (ounces) © 2011 Carnegie Learning
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Lesson 2.6 Skills Practice
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Name_________________________________________________________ Date__________________________ Use the given equations to answer each question. 13. Two catering companies host children’s sports banquets. Company A charges a fixed fee of $100 plus $3 per person. Company B charges a fixed fee of $75 plus $4 per person. The total charge for each company for any number of persons, p, can be calculated using the equations shown.
Company A: c 5 3p 1 100
Company B: c 5 4p 1 75
Which company would charge less to cater for 200 people? Company A: c 5 3(200) 1 100 5 700 Company B: c 5 4(200) 1 100 5 900 Company A would charge $200 less to cater for 200 people.
14. Lana is joining a gym. Get Fit charges $20 per month, plus a $99 initial set-up fee. Work It Out charges $30 per month, plus a $50 initial set-up fee. The equations show the total cost after any number of months, m. Get Fit: c 5 20m 1 99
Work It Out: c 5 30m 1 50
Which gym would cost less if you planned on being a member for 4 months?
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15. Theodore and Jeffrey are comparing their text messaging plans. Theodore’s cell phone company charges according to the equation c 5 5 1 0.10m. Jeffrey’s cell phone company charges according to the equation c 5 3 1 0.15m. Let c represent the total cost in dollars for m text messages sent and received. Which plan charges more to send or receive a total of 100 text messages?
16. Anthony and Lisa are both joining DVD rental programs. The cost of Anthony’s program per month can be represented by the equation c 5 10 1 1m. The cost of Lisa’s program per month can be represented by the equation c 5 5 1 2m. Let c represent the monthly cost if m DVDs are rented. Who would pay more if they each rented 7 movies in 1 month?
17. A coffee shop is ordering new coffee mugs. The total charges for The Mug Company are by c 5 25 1 0.50m. Let c represents the total cost of m mugs. If the coffee shop needs to order 100 mugs, which company should they order from?
398 • Chapter 2 Skills Practice
© 2011 Carnegie Learning
represented by the equation c 5 15 1 1.5m. The total charges for A Perfect Mug are represented
Lesson 2.6 Skills Practice
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Name_________________________________________________________ Date__________________________ 18. You are flying to visit some relatives in Boston. Budget Airline charges $150 for a round-trip ticket, plus an additional $0.20 per pound of luggage, which is represented by the equation c 5 150 1 0.20p. Let c represent the cost, and let p represent the pounds of luggage. Cheap Air charges $75 for a round-trip ticket, plus an additional $0.80 per pound of luggage, which is represented by the equation c 5 75 1 0.80p. If you are bringing 30 pounds of luggage, on which airline should you fly?
Use the given graph to answer each question. 19. You need to choose a shipping company. Ship Fast charges $2.00 per package plus $1.00 per pound. Speedy Delivery charges $3.00 per package plus $0.50 per pound. The graph of the equations that represent this situation is shown. For what package weight do both companies charge the same price? y 10 9
Shipping Cost (in dollars)
© 2011 Carnegie Learning
8 Ship Fast
7 6
Speedy Delivery
5 4 3 2 1 1
2
3
4
5
6
7
8
9
10
x
Weight (in pounds)
A package weighing 2 pounds will cost the same to ship using either company.
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20. Tate is ordering flour for her bakery. Baker’s Supplies charges $0.30 per pound, plus a $10 delivery fee. Best Flour charges $0.80 per pound, but delivery is free. The graph of the equations that represent this situation is shown. For what weight of flour is the cost equal for both companies? y 30 27
Charge (in dollars)
24 21 18 15
Baker’s Supplies
12 9 6
Best Flour
3 3
6
12
9
15
18
21
24
27
30
x
Weight (in pounds)
21. Franklin is buying fabric. For the same material, Sew Right charges $4.00 per yard and an initial $5.00 convenience fee. Stitch Plus charges $6.00 per yard and a $2.00 convenience fee. The graph of the equations that represent this situation is shown. Which store should he buy the fabric from if he is buying 5 yards of material? y 30 27
Charge (in dollars)
© 2011 Carnegie Learning
Stitch Plus
24
Sew Right
21 18 15 12 9 6 3 1
2
3
4
5
6
Length (in yards)
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Name_________________________________________________________ Date__________________________ 22. An ice cream shop is choosing a milk delivery service. The Spotted Cow charges $2.80 per gallon plus a $2 delivery fee. Dairy Farms charges $2.10 per gallon plus a $10 delivery fee. The graph of the equations that represent this situation is shown. Who charges more to deliver 15 gallons of milk? y 50 45
Charge (in dollars)
40 35 30
Dairy Farms
25 20 15 Spotted Cow
10 5 3
6
9
12
15
18
21
24
27
30
x
© 2011 Carnegie Learning
Gallons of Milk
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23. Aiko is trying to select a prepaid cell phone. The Texnel phone costs $15 per month plus $0.15 per minute. The Konia phone costs $25 per month plus $0.05 per minute. The graph of the equations that represent this situation is shown. If Aiko plans to talk an average of 150 minutes per month, which plan should she choose? 50
y
45 40
Cost of Plan ($)
35 30
Konia
25 Texnel
20 15 10 5 0
x 0
20
40
60
80 100 120 140 160 180 200 Minutes Used
24. A middle school principal is trying to select a publisher for the student handbook. Page One Publishing charges a start-up fee of $50 plus $0.75 per handbook printed. Page Two Publishing charges a start-up fee of $200 plus $0.25 per handbook printed. The graph of the equations that represent this situation is shown. Which publishing company should the principal choose if the school plans to print 200 handbooks? 500
y
450
© 2011 Carnegie Learning
400
Printing Cost ($)
350 300 Page Two
250 200
Page One
150 100 50
x
0 0
402 • Chapter 2 Skills Practice
50 100 150 200 250 300 350 400 450 500 Number of Handbooks Printed
Lesson 2.7 Skills Practice Name_________________________________________________________ Date__________________________
What, Not Lines? Introduction to Non-Linear Functions
Vocabulary Sketch a graph of each given function. 1. absolute value function
2. square or quadratic function
y
3. cube or cubic function
y
y
x
x
x
Problem Set Complete the table for each given function and use the values to graph the function. 1. y 5 |x| 1 3
© 2011 Carnegie Learning
y
x
y 5 |x| 1 3
26
9
23
6
21
4
0
3
1
4
8 6 4 2 x
0 -8
-6
-4
0
-2
2
4
6
8
-2 -4 -6
3
6
6
9
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2. y 5 __ 1 x2 2
x
y
1 2 y 5 __ x 2
8 6
24
4
22
2 x
0
21 -8
-6
-4
0
-2
2
4
6
8
2
4
6
8
-2
0
-4
1
-6
3
-8
4
3. y 5 x3 2 2 y
x
y 5 x3 2 2
8
6
22
4
21.5
2 -6
-4
0
-2 -2 -4
1 1.2 1.7 2
404 • Chapter 2 Skills Practice
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0
x
0
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Lesson 2.7 Skills Practice
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Name_________________________________________________________ Date__________________________ 4. y 5 __ 1 |x| 2
x
y
1 y 5 __ |x| 2
8 6
28
4
24
2 x
0
22 -8
-6
-4
0
-2
2
4
6
8
-2
0
-4
2
-6
4
-8
8
5. y 5 x2 24
y
x
y 5 x2 24
8 6
23
4 © 2011 Carnegie Learning
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2 -8
0 1
x
0
21 -6
-4
0
-2
2
4
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-2 -4 -6
2
-8
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6. y 5 __ 1 x3 2
x
y
1 3 y 5 __ x 2
8 6
22.5
4
22
2 x
0
21 -8
-6
-4
0
-2
2
4
6
8
-2
0
-4
1
-6
2
-8
2.5
7. y 5 2|x|
y
x
y 5 2|x|
8 6
25
4
23
2
1
-6
-4
0
-2 -2 -4 -6
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406 • Chapter 2 Skills Practice
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2
4
6
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0
x
0
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Lesson 2.7 Skills Practice
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Name_________________________________________________________ Date__________________________ 8. y 5 __ 1 x2 4
x
y
1 y 5 __ x2 4
8 6
26
4
24
2 -8
0 2
x
0
22 -6
-4
0
-2
2
4
6
8
-2 -4 -6
4
-8
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Chapter 2 Skills Practice • 407
© 2011 Carnegie Learning
408 • Chapter 2 Skills Practice
