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
A sequence is a pattern involving an ordered arrangement of numbers, geometric figures,
letters, or other objects.
2. term
A term is an individual number, figure, or letter in a sequence.
3. ellipsis
An ellipsis is three periods which mean “and so on.”
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?
Q
© 2011 Carnegie Learning
18
3. i, ii, iii, iiii, iiiii, …
4. What is the eighth term?
What is the twentieth term?
iiiiiiiiiiiiiiiiiiii
,
,
,
,
,...
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?
XI
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.
6, 5, 4, 3, 2, 1. Twenty-one 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
page 3
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
6, 10, 14, 18, 22, 26, 30, 34
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
larger cube that can be made. Include at least 6 terms in the sequence.
© 2011 Carnegie Learning
1, 8, 27, 64, 125, 216 . . .
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.
3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23
Clayton needs 46 rods to make both sides of the trestle bridge.
Chapter 2 Skills Practice • 357
Lesson 2.1 Skills Practice
page 4
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?
Cuts: 1, 2, 4, 8
Slices: 4, 8, 16, 32
Keisha should make a total of 15 cuts 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
© 2011 Carnegie Learning
10 gal 3 8 pt/gal 5 80 pt
Lesson 2.1 Skills Practice
page 5
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.
6, 12, 19, 26, 34, 42, 51, 60, 70, 80, 91, 102
It will take the runner 102 minutes (or 1 hour and 42 minutes) 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.
700, 668, 636, 604, 572, 540, 508, 476, 444, 412, 380, 348, 316, 284, 252, 220, 188, 156, 124, 92,
60, 28, 24
It took the penny about 22 seconds to hit the ground.
16. Samuel earns $30 per week for mowing grass on Mondays. He also spends $8 per week on comic
© 2011 Carnegie Learning
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?
0, 30, 22, 52, 44, 74, 66, 96, 88, 118, 110, 140, 132, 162, 154, 184, 176, 206
It will take Samuel just over 8 weeks to save $200.
Chapter 2 Skills Practice • 359
Lesson 2.1 Skills Practice
page 6
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).
Collections each day: 20, 25, 30, 35, 40, 45, 50, 55, 60, 65
Total collections: 20, 45, 75, 110, 150, 195, 245, 300, 360, 425
They collected 425 books.
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
that shows the population at the start of each year during the study.
© 2011 Carnegie Learning
8000, 4000, 2000, 1000, 500, 250, 125
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.
A discrete graph is a graph that consists of isolated points. A continuous graph is a graph with
no breaks in it.
2. Explain the difference between a graph that is linear and a graph that is nonlinear.
A linear graph is a graph that is a line or a series of collinear points. A nonlinear graph is a
graph that is not a line and not a series of collinear points.
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
7
7
6
6
5
5
4
4
3
3
2
2
1
1
1
2
3
4
5
6
7
8
9
10
The graph is discrete and decreasing.
x
1
2
3
4
5
6
7
8
9
10
x
The graph is continuous and both increasing and decreasing.
Chapter 2 Skills Practice • 361
Lesson 2.2 Skills Practice
3.
page 2
4.
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 graph is discrete and neither The graph is continuous and decreasing.
increasing nor decreasing.
6.
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
The graph is continuous and both decreasing and increasing.
362 • Chapter 2 Skills Practice
10
x
1
2
3
4
5
6
7
8
9
10
x
The graph is continuous and increasing.
© 2011 Carnegie Learning
5.
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
2
3
4
5
6
7
8
9
10
x
1
2
3
4
5
6
7
8
9
10
x
The graph is linear and increasing.
The graph is linear and neither increasing nor decreasing.
© 2011 Carnegie Learning
9.
10.
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
The graph is nonlinear and both The graph is nonlinear and neither increasing and decreasing.
increasing nor decreasing.
10
x
Chapter 2 Skills Practice • 363
Lesson 2.2 Skills Practice
11.
page 4
y
10
9
8
7
6
5
4
3
2
1
1
2
3
4
5
6
7
8
9
10
x
The graph is linear and increasing.
12.
y
10
9
8
7
6
5
4
3
2
1
2
3
4
5
6
7
8
9
10
The graph is nonlinear and increasing.
364 • Chapter 2 Skills Practice
x
© 2011 Carnegie Learning
1
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
The rocket rose quickly to a peak height
y
and then slowly dropped back down to
Height of rocket
the ground.
x
Second
15.
The amount of heating oil used increased
y
over a short time, slowly decreased, and
then increased quickly again. Perhaps
the weather turned cold quickly, slowly
x
Day
366 • Chapter 2 Skills Practice
© 2011 Carnegie Learning
Heating oil used
warmed, and then got cold again.
Lesson 2.2 Skills Practice
page 7
Name_________________________________________________________ Date__________________________
16.
Jason’s savings increased at a steady
y
rate, fell off quickly, and then increased
steadily again. Perhaps Jason withdrew
Jason’s savings account balance
a large amount of money from savings to
make a purchase and then started
building his savings again.
x
Month
17.
Dan steadily increased the distance he
y
ran and then ran the same distance for a
few days. He suddenly stopped running
completely and then increased his
© 2011 Carnegie Learning
Distance Dan ran
distance slowly. Perhaps he was sick or
had an injury that caused him to stop
running and had to start back slowly.
x
Day
Chapter 2 Skills Practice • 367
Lesson 2.2 Skills Practice
18.
page 8
The puppy grew steadily for months
y
until he reached his full-grown weight,
which he maintained, though it
Weight of a puppy
fluctuated slightly.
x
© 2011 Carnegie Learning
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)
relation
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)
function
5. A(n)
scatter plot
6. The
vertical line test
input
output
.
.
maps each input to one and only one output.
is a graph of a collection of ordered pairs.
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)
mapping
shows objects in two sets connected together to represent a relationship
between the two sets.
© 2011 Carnegie Learning
8. A(n)
set
is a collection of numbers, geometric figures, letters, or other objects that
have some characteristic in common.
9. The
domain
10. The
range
of a function is the set of all inputs of the function.
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.
1
2
3
4
4
6
8
10
(1, 4), (2, 6), (3, 3), (3, 5), (4, 4), (4, 6)
The relation is a function.
The relation is not a function.
4.
5
3
4
5
6
(1, 4), (2, 6), (3, 8), (4, 10)
3.
1
2
3
4
6
10
7
20
8
30
10
(5, 20), (6, 10), (7, 10), (8, 30), (10, 30)
The relation is a function.
Input
Output
4
8
8
12
12
16
16
20
20
24
(4, 8), (8, 12), (12, 16), (16, 20), (20, 24)
.
The relation is a function
370 • Chapter 2 Skills Practice
© 2011 Carnegie Learning
2.
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
(15, 0), (10, 5), (5, 10), (10, 15), (15, 20)
(0, 15), (5, 10), (10, 5), (15, 10), (20, 15)
The relation is not a function.
The relation is a function.
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. The scatter plot is a function. No vertical
A vertical line can be drawn through lines cross more than one point.
(4, 1) and (4, 5).
Chapter 2 Skills Practice • 371
Lesson 2.3 Skills Practice
9.
page 4
10.
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. The graph is not a function. A vertical line A vertical line can be drawn through will cross two y-values for most x-values.
(3, 2) and (3, 6).
12.
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 graph is a function. No vertical line The graph is not a function. A vertical line will cross two y-values for any x-value.
will cross two y-values for most x-values.
372 • Chapter 2 Skills Practice
© 2011 Carnegie Learning
11.
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
The equation is a function.
The equation is a function.
______
16. y 5 ​√ x 1 5 ​ 
15. y2 5 x
The equation is not a function. For example,
3 5 9 and (23) 5 9. Each x-value except 0
The equation is not a function. For example,
______
______
​and 23 5 √
​ 4 1 5  
​. Each x-value
3 5 ​√4 1 5  
can be mapped to two y-values.
except 25 can be mapped to two y-values.
2
2
17. y 5 2|x|
__
18. ​√y  ​5 x 2 8
The equation is a function.
The equation is a function.
1  ​x
19. y 5 ​ __
2
20. | y| 5 6 1 4x
The equation is a function.
The equation is not a function. For example,
|10 | 5 6 1 4(1) and |210 | 5 6 1 4(1).
Each x-value greater than 21.5 can be
© 2011 Carnegie Learning
mapped to two y-values.
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
page 6
22. Input: There is 1 copy of a popular book in the library.
Output: The book has been checked out by 45 different people.
No. One book is mapped to 45 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.
No. One memo is mapped to 28 teachers.
24. Input: There are 13 cats for adoption at the animal shelter.
Output: Each cat is adopted by a different family.
Yes. Each family adopts just 1 cat.
25. Input: There are 3 showings of a play.
Output: Over 200 people attend each showing.
No. Each showing is mapped to over 200 people.
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.
No. The new issue is mailed 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.
Yes. Each school day Yi Ling has only 1 language class.
374 • Chapter 2 Skills Practice
© 2011 Carnegie Learning
Yes. Each cookie is bought by just 1 person.
Lesson 2.4 Skills Practice
Name_________________________________________________________ Date__________________________
Scaling a Cliff
Linear Functions
Vocabulary
Define the term in your own words.
1. linear function
A function whose graph is a straight line is a 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.
2. Rosita’s pet rabbits eat 12 ounces of rabbit food every day.
The number of ounces of rabbit food eaten is the dependent quantity. The number of days is
© 2011 Carnegie Learning
the independent quantity.
3. The amount of electricity used by a light changes as the knob on the dimmer switch is turned.
The amount of electricity used by the light is the dependent quantity. The position of the dimmer switch is the independent quantity.
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.
The total amount of money she raises for the troop is the dependent quantity. The number of
boxes she sells is the independent quantity.
5. The height reached by a water-propelled rocket is directly related to the amount of water pressure
within the rocket.
The height reached by the rocket is the dependent quantity. The amount of water pressure in
the rocket is the independent quantity.
6. As an engineer opens the release gate on a dam’s spillway, the amount of water released from the
lake increases.
The amount of water released from the lake is the dependent quantity. The amount the release
© 2011 Carnegie Learning
gate is opened is the independent quantity.
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
© 2011 Carnegie Learning
27
18
15
12
9
6
3
0
0
1
2
3
4
5
6
7
8
9
10
Time (hours)
Chapter 2 Skills Practice • 377
Lesson 2.4 Skills Practice
page 4
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
Quantity Name
Time
Diameter
Unit of Measure
Weeks
Inches
0
6
1
8
3
12
5
16
10
26
t
2t 1 6
Expression
30
27
21
18
© 2011 Carnegie Learning
Pumpkin Diameter (inches)
24
15
12
9
6
3
0
0
1
2
3
4
5
6
Time (weeks)
378 • Chapter 2 Skills Practice
7
8
9
10
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
Time
Water Level
Unit of Measure
Minutes
Centimeters
1
15
4
30
8
50
12
70
15
85
t
5t 1 10
Expression
100
90
Water Level (centimeters)
© 2011 Carnegie Learning
80
70
60
50
40
30
20
10
0
0
2
4
6
8
10
12
14
16
18
20
Time (minutes)
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
Time
Account Balance
Unit of Measure
Weeks
Dollars
1
185
3
155
5
125
8
80
10
50
w
200 2 15w
Expression
200
180
140
120
100
80
60
40
20
0
0
2
4
6
8
10
12
Time (weeks)
380 • Chapter 2 Skills Practice
14
16
18
20
© 2011 Carnegie Learning
Account Balance (dollars)
160
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
Time
Number of Rotations
Unit of Measure
Seconds
Rotations
1
6
5
30
12
72
30
180
50
300
t
6t
Expression
300
270
240
Number of Rotations
© 2011 Carnegie Learning
210
180
150
120
90
60
30
0
0
5
10
15
20
25
30
35
40
45
50
Time (seconds)
Chapter 2 Skills Practice • 381
Lesson 2.4 Skills Practice
page 8
12. A corn mill produces 1 ounce of cornmeal with every 4 rotations of the stone-grinding wheel.
Independent
Quantity
Dependent
Quantity
Quantity Name
Rotations
Cornmeal Produced
Unit of Measure
Rotations
Ounces
4
1
12
3
20
5
36
9
40
10
r
1  ​r
​ __
4
Expression
10
9
7
6
5
4
3
2
1
0
0
4
8
12
16
20
24
Number of Rotations
382 • Chapter 2 Skills Practice
28
32
36
40
© 2011 Carnegie Learning
Cornmeal Produced (ounces)
8
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
Time
Concrete Remaining
in Truck
Unit of Measure
Seconds
Cubic Yards
10
68
20
66
50
60
100
50
200
30
t
70 2 0.2t
Expression
100
90
Concrete Remaining in Truck
(cubic yards)
© 2011 Carnegie Learning
80
70
60
50
40
30
20
10
0
0
20
40
60
80
100 120 140 160 180 200
Time (seconds)
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
Time
Distance Travelled
Unit of Measure
Seconds
Feet
5
17.50
10
35
25
87.50
50
175
100
350
t
3.5t
Expression
350
315
245
210
175
140
105
70
35
0
0
10
20
30
40
50
60
Time (seconds)
384 • Chapter 2 Skills Practice
70
80
90
100
© 2011 Carnegie Learning
Distance Travelled (feet)
280
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
80 1 5(500) 5 2580
6
80 1 6(500) 5 3080
7
80 1 7(500) 5 3580
8
80 1 8(500) 5 4080
9
80 1 9(500) 5 4580
10
80 1 10(500) 5 5080
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
55 1 30(2) 5 115
4
55 1 30(4) 5 175
6
55 1 30(6) 5 235
8
55 1 30(8) 5 295
10
55 1 30(10) 5 355
12
55 1 30(12) 5 415
4. Mr. Cloud is writing an autobiography. He has already written 32 pages. Each day, he writes
Number of Days
Number of Pages Written
10
32 1 5(10) 5 82
15
32 1 5(15) 5 107
20
32 1 5(20) 5 132
25
32 1 5(25) 5 157
30
32 1 5(30) 5 182
35
32 1 5(35) 5 207
386 • Chapter 2 Skills Practice
© 2011 Carnegie Learning
another 5 pages.
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
(70, 1600)
1400
(60, 1300)
1200
1000
(50, 1000)
800
(40, 700)
600
400
(30, 400)
200
(20, 100)
10
1600
20
30
40
50
60
80
70
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.
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
900
Total Paper Costs (in dollars)
© 2011 Carnegie Learning
c
1000
800
700
(16, 655)
600
(14, 585)
500
(12, 505)
(10, 425)
400
(8, 345)
300
(6, 265)
200
14
585
16
665
100
2
4
6
8
10
12
14 16
18
20
r
Number of Reams Delivered
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.
w
Total Number of
Windows
50
110
75
160
100
210
125
260
150
310
175
360
500
450
400
Total Number of Windows
Number of
Hotel Rooms
(175, 360)
350
(150, 310)
300
(125, 260)
250
(100, 210)
200
(75, 160)
150
(50, 110)
100
50
20
40
60
80 100 120 140 160 180 200
r
Number of Hotel Rooms
8. A bookstore spends $300 on a new shipment of 200 books. They sell each book for $12.
They record their total profit, p, in dollars, after selling b books.
p
40
180
60
420
80
660
100
900
120
1140
140
1380
388 • Chapter 2 Skills Practice
1800
1600
1400
(140, 1380)
1200
(120, 1140)
1000
(100, 900)
800
(80, 660)
600
(60, 420)
400
200
(40, 180)
20
40
60
80 100 120 140 160 180 200
Number of Books Sold
b
© 2011 Carnegie Learning
Total Profit
(in dollars)
Total Profit (in dollars)
Number of
Books Sold
2000
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?
200 1 1(90) 5 200 1 90 5 290
If Evan waits 90 days to pay back his parents, he will owe them a total of $290.
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
yearly cost, in dollars, for the 200 cases of water?
© 2011 Carnegie Learning
50 1 5(200) 5 50 1 1000 5 1050
The café owner’s total yearly cost is $1050 for 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?
30 1 2(350) 5 30 1 700 5 730
The total cost will be $730 if 350 magazines are ordered per month.
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?
_________  ___ 
12 89 ​ 5
  11.125
​ 101 2 ​ 5 ​ 
8
8
Because the answer is a decimal, I estimated that after about 11 days, 101 people will 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
the party?
_______  ___ 
4  30 ​ 5
  10
​ 34 2 ​ 5 ​ 
3
3
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?
_______  ___ 
7  13 ​ 5
  6.5
​ 20 2 ​ 5 ​ 
2
2
Because Sean cannot visit half of a art gallery, he will need to visit 7 galleries to own at least 20 paintings.
390 • Chapter 2 Skills Practice
© 2011 Carnegie Learning
Ten people are attending the party if he orders 34 slices of pizza.
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.
s 5 500 1 15t
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.
s 5 60,000 1 5000t
20. A hair stylist earns $70 per day, plus $20 for each haircut. Write an equation that relates his total
daily income d, in dollars, for any number of haircuts, h.
© 2011 Carnegie Learning
d 5 70 1 20h
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.
c 5 5b 1 8
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.
b 5 2s 1 10
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
The point of intersection is the point at which two lines on a graph intersect. This indicates
where two data points are equivalent to each other.
2. estimation
Estimation is the process of determining the approximate value of an expression, often done
through rounding.
Problem Set
Estimate each value of each expression. Then, calculate the exact value.
1. 750.25 1 225.50
975; 975.75
© 2011 Carnegie Learning
3. 25 3 101
2500; 2525
2. 1.98 1 1.73
4; 3.71
4. 236 3 4
960; 944
5. 146.9 2 92.5
6. 4261 2 2637
60; 54.4
1700; 1624
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
Year
Job C
Job D
1
$40,000 1 $3000 5 $43,000
$40,000
2
$40,000 1 $1500 5 $41,500
$40,000 3 1.05 5 $42,000
3
$41,500 1 $1500 5 $43,000
$42,000 3 1.05 5 $44,100
4
$43,000 1 $1500 5 $44,500
$44,100 3 1.05 5 $46,305
After 4 years, Job C has paid: $43,000 1 $41,500 1 $43,000 1 $44,500 5 $172,000
Job D has paid: $40,000 1 $42,000 1 $44,100 1 $46,305 5 $172,405
Job D will pay me more for 4 years of work.
394 • Chapter 2 Skills Practice
© 2011 Carnegie Learning
you more in total for all 4 years?
Lesson 2.6 Skills Practice
page 3
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
$6000
$6000
2
$6000 3 1.06 5 $6360
$6000 1 $370 5 $6370
3
$6360 3 1.06 5 $6741.60
$6370 1 $370 5 $6740
4
$6741.60 3 1.06 5 $7146.10
$6740 1 $370 5 $7110
After 4 years, Plan A would have a greater account balance than Plan B.
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
© 2011 Carnegie Learning
would have a greater account balance?
Month
Account A
Account B
1
$5000
$5000
2
$5000 1 $50 5 $5050
$5000 3 1.01 5 $5050
3
$5050 1 $50 5 $5100
$5050 3 1.01 5 $5100.50
4
$5100 1 $50 5 $5150
$5100.50 3 1.01 5 $5151.51
After 4 months, Account B would have a greater account balance.
Chapter 2 Skills Practice • 395
Lesson 2.6 Skills Practice
page 4
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
40
35
2
40 1 3 5 43
35 1 4.5 5 39.50
3
43 1 3 5 46
39.50 1 4.5 5 44
4
461 3 5 49
44 1 4.5 5 48.50
5
49 1 3 5 52
48.50 1 4.5 5 53
After 5 years, the average Jersey cow produces the most milk daily.
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
Week
Weight of the Patch A Pumpkin
(ounces)
Weight of the Patch B Pumpkin
(ounces)
1
13
9
2
13 1 3.2 5 16.20
9 1 3.6 5 12.60
3
16.20 1 3.2 5 19.40
12.60 1 3.6 5 16.20
4
19.40 1 3.2 5 22.60
16.20 1 3.6 5 19.80
5
22.60 1 3.2 5 25.80
19.80 1 3.6 5 23.40
After 5 weeks, the pumpkin from Patch A is the largest.
396 • Chapter 2 Skills Practice
© 2011 Carnegie Learning
show the growth for each pumpkin for 5 weeks. After 5 weeks, which pumpkin is the largest?
Lesson 2.6 Skills Practice
page 5
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?
© 2011 Carnegie Learning
Get Fit: c 5 20(4) 1 99 5 179
Work It Out: c 5 30(4) 1 50 5 170
Work It Out would cost $9 less to be a member for 4 months.
Chapter 2 Skills Practice • 397
Lesson 2.6 Skills Practice
page 6
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?
Theodore’s plan: c 5 5 1 0.10(100) 5 5 1 10 5 15
Jeffrey’s plan: c 5 3 1 0.15(100) 5 3 1 15 5 18
Jeffrey’s plan charges $3 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?
Anthony would pay: c 5 10 1 1(7) 5 10 1 7 5 17
Lisa would pay: c 5 5 1 2(7) 5 5 1 14 5 19
Lisa would pay $2 more if they each rented 7 movies.
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?
The Mug Company: c 5 15 1 1.5(100) 5 15 1 150 5 $165
A Perfect Mug: c 5 25 1 0.50(100) 5 25 1 50 5 $75
The coffee shop should order from A Perfect Mug because they will charge $90 less for an
order of 100 mugs.
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
page 7
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?
Budget Airline: c 5 150 1 0.20(30) 5 150 1 6 5 $156
Cheap Air: c 5 75 1 0.80(30) 5 75 1 24 5 $99
You should fly on Cheap Air because it will cost $57 less than flying on Budget Airline.
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.
Chapter 2 Skills Practice • 399
Lesson 2.6 Skills Practice
page 8
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)
For 20 pounds of flour, the two companies charge the same total price.
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
7
8
9
10
x
Length (in yards)
Franklin should buy from Sew Right because it charges less for 5 yards of fabric.
400 • Chapter 2 Skills Practice
Lesson 2.6 Skills Practice
page 9
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
Gallons of Milk
© 2011 Carnegie Learning
The Spotted Cow charges more to deliver 15 gallons of milk.
Chapter 2 Skills Practice • 401
Lesson 2.6 Skills Practice
page 10
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
Aiko should choose the Konia phone if she talks 150 minutes per month.
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
50 100 150 200 250 300 350 400 450 500
Number of Handbooks Printed
The principal should choose Page One Publishing to print 200 handbooks.
402 • Chapter 2 Skills Practice
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
-8
Chapter 2 Skills Practice • 403
Lesson 2.7 Skills Practice
page 2
2. y 5 __
​ 1 ​ x2
2
y
x
1 2
y 5 ​ __  ​x
 
2
8
24
8
6
22
2
21
0.50
4
2
0
0
1
0.50
x
0
-8
-6
-4
0
-2
2
4
6
8
2
4
6
8
-2
-4
-6
3
4.50
4
8
-8
3. y 5 x3 2 2
y
x
y 5 x3 2 2
22
210
21.5
¯ 25.38
21
23
8
6
4
2
22
1
21
1.2
¯ 20.27
1.7
¯ 2.91
2
6
-6
-4
0
-2
-2
-4
404 • Chapter 2 Skills Practice
-6
-8
© 2011 Carnegie Learning
0
x
0
-8
Lesson 2.7 Skills Practice
page 3
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4. y 5 __
​ 1 ​ |x|
2
y
x
1
y 5 ​ __  ​|x|
 
2
8
28
4
6
24
2
22
1
0
0
2
1
4
2
x
0
-8
-6
-4
0
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2
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-2
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2
8
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-8
5. y 5 x2 24
© 2011 Carnegie Learning
y
x
y 5 x2 24
23
5
22
0
21
23
8
6
4
2
-8
0
24
1
23
2
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3
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x
0
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4
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8
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Chapter 2 Skills Practice • 405
Lesson 2.7 Skills Practice
page 4
6. y 5 __
​ 1 ​ x3
2
x
1 3
y 5 ​ __  ​x
 
2
22.5
¯ 27.81
22
24
21
20.50
y
8
6
4
2
0
0
1
0.5
2
4
2.5
¯ 7.81
x
0
-8
-6
-4
0
-2
2
4
6
8
-2
-4
-6
-8
7. y 5 2|x|
y
x
y 5 2|x|
25
10
23
6
21
2
0
0
1
2
8
6
4
2
-8
-6
-4
0
-2
-2
-4
-6
2
4
4
8
406 • Chapter 2 Skills Practice
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-8
2
4
6
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© 2011 Carnegie Learning
Lesson 2.7 Skills Practice
page 5
Name_________________________________________________________ Date__________________________
8. y 5 __
​ 1 ​ x2
4
y
x
1
y 5 ​ __  ​ x2
4
8
26
9
6
24
4
22
1
4
2
0
0
2
1
x
0
-8
-6
-4
0
-2
2
4
6
8
-2
-4
-6
4
6
9
-8
© 2011 Carnegie Learning
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Chapter 2 Skills Practice • 407
© 2011 Carnegie Learning
408 • Chapter 2 Skills Practice