Pre-TestUnit2:LinearFunctionsKEY
Please do not use a calculator. No calculator necessary.
Define variables and create an equation to model each of the following situations. (4 pts; 2 pts for
variable definitions, 2 pts for correct equation)
1. You start the day with $22 in your pocket and then
sell ears of corn for $4 each.
2.
ears of corn sold
money made based on corn sold
4 22
3.
Time racing
in seconds
Distance
traveled in
meters
input
output
2
4. 2, 1.5, 1, 0.5, 0, 0.5, 1 …
0
2
4
6
8
0
3
6
9
12
time racing in seconds
distance traveled in meters based on time racing
term number beginning at 0
term value
2
Create a graph representation of the following linear functions. (4 pts; partial credit at teacher discretion)
5. Watch batteries cost $2.50 for three batteries
but there was a $2 discount on the total order.
6. 2 5
Describe the transformation that takes for each function as compared to the function ! ".
(4 pts; partial credit at teacher discretion)
7. 3
8. 3
Translates the function up three units
Pushes the graph three times closer to the -axis
Identify the rate of change and initial value in each function and then describe the rate of change and initial
value in context. (4 pts; 1 pt for each)
Total cost
9. The function relating the cost in dollars of entering a carnival, , to how many tickets you buy, , is shown by
the following graph:
Rate of Change:__0.5________
ROC in Context:_It costs $1 for two tickets or $0.50 per ticket______
Initial Value:___$3__________
IV in context:__There is a $3 fee no matter what, probably an entrance fee ___
Number of tickets bought
10. The amount of money in dollars a farmer gets paid, #$, to leave land fallow for a season based on the acres
of land he or she owns, $, is modeled by the following function: # 300$ 50.
Rate of Change: __300______
ROC in Context: __The gets $300 per acre left fallow_______________
Initial Value: ____50______
IV in Context: _There is a $50 fee possibly to enroll in the program____
Write and solve an equation for the following situations. (4 pts; 1 pts for correct equation, 2 pts for
correct simplification and inverse operations, 1 pt for answer)
11. A man buys four books from the store and a Preferred Reader discount card for $20. Later that day, he goes
back and buys five more books. He also got a $5 discount using his new card. If he spent a total of $87 at the
bookstore, how much did each book cost assuming every book cost the same amount?
4& 20 5& 5 87
& $8
12. A man bought 4 cups of coffee and left a $7 tip. A woman bought 8 cups of coffee and only left a $2 tip. If
they paid the same amount, how much was each cup of coffee?
4 7 8 2
$1.25
Answer the following questions comparing linear functions. (4 pts; 2 pts for answer, 2 pts for explanation)
NASA is testing a series of new rockets to decide which one to use for the upcoming Moving to Mars Mission.
Here is the information about the power consumption (#) in kW of electricity in terms of time () in hours of
each rocket.
Power consumption is modeled by the equation # 1.6
Rocket B:
Power consumption is modeled in the following table
2
4
6
8
10
#
5
8
11
14
17
Rocket C:
Power consumption graph
Power in kW )
Rocket A:
Time in Hours (
Rocket D:
Consumes approximately 14 kW in 10 hours plus an initial 3 kW at lift off
13. Which rocket uses the most power per hour and how do you know?
Rocket A uses only 1.6 KW per hour while the others use 1.5, 0.8 and 1.4 KW per hour respectively.
14. Which rocket uses the most power at lift off (initially) and how do you know?
Rocket C uses 4 KW initially while the others use 0, 2 and 3 KW respectively.
Solve the following equations for the given variable. There may be a single solution, infinite
solutions, or no solutions. (4 pts; 2 pts for work, 2 pts for answer)
15. 7' 3' 10 3 43
16. 4 2 22
'5
4
17. 6
9 7 4
12
18. 6& 2 6& 13
5
+,+-./+
0
19. 6
9 4
12
20. 6& 2 6& 12
+,+-./+
///1,+-./+,
Find the inverse function of the given function. (4 pts; 2 pts for work, 2 pts for answer)
21. 4
2
8
2 3
3
Solve the following inequalities and graph the solutions on the number line. (4 pts; 2 pts for answer,
2 pts for graphing solution on number line)
22.
0
234
38
23. 2 2 4 8
5 5
Graph the following inequalities on the coordinate plane. (4 pts; 2 pts for line placement and type,
2 pts for shading)
24. 3 4
25. 5 3 7
Lesson 2.1
2.1
Unit 2 Homework Answer Key 23
Graph the following linear equations using slope-intercept form.
1. 2 1
2. 3 4
3. 5
4. 7
5. 3 2
6. 5
7. 6 2
8. 0 1
9. 4
10. 2 2
11. 3 4
12. 4 5
13. 4 2
6
14. 6 3
9
15. 3
6
16. 2 3
12
17. 4 2
8
18. 2 3
9
Use the given functions to describe the listed transformations. Then write the equation of the transformed
function.
3 − 2
' = −2 + 4
ℎ = 5
19. 2
20. 2 ∗ 21. − 2
Stretched twice as close to the -axis
2 = 6 − 2
Stretched 2 x far away from -axis
2 ∗ = 6 − 4
Translated down 2 units
− 2 = 3 − 4
22. + 2
23. '−
24.
Translated left 2 units
+ 2 = 3 + 4
Reflected across -axis
'− = 2 + 4
Half as far away from the -axis
∗ ' = − + 2
25. ' + 5
26. ' − 5
27. Translated up 5 units
Translated right 5 units
28. −3 ∗ '
29. ℎ − 4
30. ℎ + 6
Reflected across -axis
Stretched 3 times as far away
from the -axis
−3 ∗ ' = 6 − 12
Translated down 4 units
No translation
since it is a horizontal line
ℎ − 4 = 1
ℎ + 6 = 5
31. ℎ2
32. 2 ∗ ℎ
33. − 3
No translation
since it is a horizontal line
ℎ2 = 5
Stretched twice as far away
from the -axis
2 ∗ ℎ = 10
Translated down 3 units
' + 5 = −2 + 9
' − 5 = −2 + 14
∗
'
Stretched half as close to the -axis
8 9 = − 2
− 3 = 3 − 5
Lesson 2.2
Identify the rate of change, initial value, independent variable, and dependent variable. Then describe what
the rate of change and initial value mean in the context of each situation. Finally, write the equation of each
linear function.
1. A 2.5 foot rocket’s distance traveled in meters based on time in seconds is modeled by the following
function: 5 2.
Rate of Change:__5__________
Initial Value:___2___________
Independent Variable:_____
Contextual Description of
Rate of Change
Contextual Description of
Initial Value
The rocket travels 5 meters
per second,
Before the rocket launches
(when time is 0), it is two
meters off the ground.
Dependent Variable:________
2. The cost for 6 people to travel in a taxi in New York based on the number of miles driven is shown by
the following graph:
Rate of Change:___________
Cost ($)
Initial Value:__2____________
Independent Variable:______
Dependent Variable:________
Contextual
Description of
Rate of Change
Contextual
Description of
Initial Value
The taxi charges one
dollar per two miles
traveled.
A passenger is
charged $2 flat fee
to use the taxi.
EQ of Line:___ 2 ____
Miles driven
3. Planet Wiener receives $2.25 for every hotdog sold. They spend $105 for 25 packages of hot dogs and 10
packages of buns. Think of the linear function that demonstrates the profit # based on the number of hotdogs
sold .
Rate of Change:___2.25________
Contextual Description of
Rate of Change
Contextual Description of
Initial Value
Planet Wiener makes $2.25
for every hotdog sold.
Planet Wiener spends $105
on food and supplies.
Initial Value:____105__________
Independent Variable:______
Dependent Variable:___#_____
EQ of Line:_# 2.25 105 _
4. The weight (in pounds) of a 20′ x 10” x 12” aquarium tank < based on the number of gallons of water inside
' is modeled by the following function: < 8.5' 20.
Rate of Change:___8.5_________
Initial Value:_____20__________
Independent Variable:__'____
Contextual Description of
Rate of Change
Contextual Description of
Initial Value
Each gallon of water weighs
8.5 pounds.
The tank weighs 20 pounds
without water in it.
Profit
Dependent Variable:__<______
5. The amount of profit of the lemonade stand on 120 W Main Street # based on the number of glasses of
lemonade sold ' is modeled by the following graph:
Contextual
Contextual
Rate of Change:____ _______
Description of
Description of
0
Rate of Change
Initial Value
Initial Value:____3__________
If the sellers sell 0
The sellers make 0
Independent Variable:__'____
glasses of
of a dollar ($0.75)
lemonade, they will
per glass of
Dependent Variable:____#____
have lost $3
lemonade sold.
EQ of Line:___# 0 ' 3 ___
Number of glasses sold
6. A candle starts at a height of 5 inches and diameter of 3 inches and burns down 1 inch every 2 hours. Think of
the linear function that demonstrates the height of the candle in terms of the time it has been burning .
Rate of Change:___ ________
Initial Value:____5__________
Independent Variable:______
Dependent Variable:________
EQ of Line:___ 5 ___
Contextual Description of
Rate of Change
Contextual Description of
Initial Value
The candle burns 1 inch
every 2 hours.
The candle starts at a height
of 5 inches.
7. The cost to stay in a 4 star hotel each night is modeled by the following function: 104 15
Rate of Change:___104_________
Initial Value:____15___________
Independent Variable:______
Contextual Description of
Rate of Change
Contextual Description of
Initial Value
It costs $104 each night
There is a $15 fee.
Dependent Variable:________
Cost
8. The cost to attend a sports clinic 37 miles away based on the number of days attended is modeled by
the following graph:
Contextual
Contextual
Rate of Change:___25________
Description of
Description of
Rate of Change
Initial Value
Initial Value:____0__________
Independent Variable:______
Dependent Variable:________
It costs $25 per day
to attend the sports
clinic.
There is no initial
value.
EQ of Line:__ 25___
Days
9. A dog kennel charges $40 for each night the dog stays in the kennel. Each day includes a 2 hour play time and
1 hour etiquette training. The kennel also charges a $10 bathing fee for a bath before the dog returns home.
Think of the linear function that demonstrates the cost of putting a dog in the kennel in terms of the number
of nights .
Rate of Change:___40________
Contextual Description of
Rate of Change
Contextual Description of
Initial Value
It costs $40 per night.
There is a $10 bathing fee.
Initial Value:___10___________
Independent Variable:______
Dependent Variable:________
EQ of Line:___ 40 10 __
10. The number of gallons of gas in your 15 gallon gas tank ' based on the number of miles traveled is
modeled by the following function: ' 12.
6
Rate of Change:___
Contextual Description of
Rate of Change
Contextual Description of
Initial Value
The car uses 1 gallons of gas
every 25 miles.
12 gallons of gas are in the
tank to begin with.
_________
6
Initial Value:___12____________
Independent Variable:______
Dependent Variable:___'_____
11. The number of pizzas ordered for 8th grade night # based on the number of students , is shown by the
following graph:
Number of pizzas
Rate of Change:__0_________
Initial Value:____2__________
Independent Variable:__,____
Dependent Variable:___#_____
EQ of Line:___# 0 , 2 ____
Contextual
Description of
Rate of Change
0
of a pizza was
ordered for each
student, or 1 pizza
was ordered for
every 4 students.
Contextual
Description of
Initial Value
2 pizzas are ordered
when there are 0
students.
Number of students
12. It costs $5.50 to mail a large package to New Zealand. The post office will weigh your package and charge
you an extra $0.30 per pound. The delivery takes 2 weeks. Think of the linear function that demonstrates the
cost to mail a large package to New Zealand based on the number pounds it weighs #.
Rate of Change:___0.30________
Contextual Description of
Rate of Change
Contextual Description of
Initial Value
A package sent to New
Zealand costs $0.30 per
pound of weight.
It costs $5.50 to mail a
package that weighs 0
pounds.
Initial Value:_____5.50_________
Independent Variable:__#____
Dependent Variable:________
EQ of Line:___ 0.30# 5.50 __
13. An author wrote an 876-page book. The amount of profit # based on the number books sold & is
modeled by the following function: # 7& 1050.
Rate of Change:___7_________
Contextual Description of
Rate of Change
Initial Value:____1050___________ There is a $7 profit for each
Independent Variable:__&____
book sold.
Contextual Description of
Initial Value
There is a $1050 profit
when no books are sold.
Grade earned
Dependent Variable:___#_____
14. The average grade earned on the Unit 3 test ' based on the number of hours of studying is modeled by
the following graph:
Contextual
Contextual
Rate of Change:___10________
Description of
Description of
Rate of Change
Initial Value
Initial Value:____40__________
Independent Variable:______
Dependent Variable:__'______
A student earns an
extra 10% for every
hour of studying.
A student earns
40% when he/she
studies for 0 hours.
EQ of Line:__' 10 40 ___
Hours of studying
15. Kiley invited 32 people to her 13th birthday party at the bowling alley. She hopes most people can come! It
costs $40 to reserve the bowling alley. It will cost an additional $2 per friend to bowl. Think of the linear function
that demonstrates the cost of the birthday party in terms of the number of friends who attend and bowl .
Rate of Change:___2________
Contextual Description of
Rate of Change
Contextual Description of
Initial Value
It costs $2 per friend to
bowl.
It costs $40 if 0 friends
bowl.
Initial Value:___40___________
Independent Variable:______
Dependent Variable:________
EQ of Line:___ 2 40 __
16. You started a mowing business so you could buy a 2015 Chevy Camaro when you turn 16. The amount of
money in your bank account based on the number of yards you mow is modeled by the following
function: 30
.
Rate of Change:___30_________
Initial Value:____0___________
Independent Variable:__
____
Contextual Description of
Rate of Change
Contextual Description of
Initial Value
You earn $30 for each yard
you mow.
You have $0 in your account
before you mow any yards.
Temperature
Dependent Variable:________
17. When an oven is set at 350>, the internal temperature of a chicken breast after every minute it’s in
the oven is modeled by the following graph:
Contextual
Contextual
Rate of Change:___5________
Description of
Description of
Rate of Change
Initial Value
Initial Value:____40__________
Independent Variable:______
Dependent Variable:________
The temperature
increases 5> every
minute it’s in the
oven.
The chicken breast
is 40> before it
goes in the oven.
EQ of Line:__ 5 40 ___
Minutes
18. Walter’s Water Adventures charges $34 to enter. This fee helps pay for maintenance and lifeguards. They
always have 3 lifeguards at each slide plus 2 watching the wave pool. Think of the linear function that
demonstrates the number of lifeguards on duty - based on the number of slides open , on a given day.
Rate of Change:___3________
Contextual Description of
Rate of Change
Contextual Description of
Initial Value
There are 3 lifeguards for
each slide.
There are 2 lifeguards at the
wave pool
Initial Value:___2___________
Independent Variable:__,____
Dependent Variable:__-______
EQ of Line:___- 3, 2 __
Lesson 2.3A
Use the given equation to solve the questions.
1. If a roller coaster starts 12 meters above the ground and climbs 2 meters every second ,, the roller coaster’s
height would be based on the equation 2, 12. How long would it take to reach the top of the hill
that is 80 meters above the ground?
34 seconds
2. If it is going to cost you $525 dollars to start a lawn care business with your friend, but you will earn an average
?
of $73 for every 4 yards , your profit # is based on the equation # 0 525. How much profit
would you make if you were scheduled to mow 48 yards the first summer?
$351
3. The CMS dance team is hosting a car wash fundraiser and charging $3 per car. If the dance team washed a
total of 14 cars , how much money did the team make if you followed the equation 3?
$42
4. If you spent $10.35 total purchasing songs online for $1.15 each, how many songs did you buy , if you
followed the equation 1.15,?
9 songs
5. Your running pace is 1 mile every 8 minutes. If you ran a distance of 5.5 miles, how many minutes were you running if you followed the equation @ ?
44 minutes
6. If CMS orders 25 cartons of milk plus 1 for every 3 students , eating lunch, the number of cartons of
milk they order is based on the equation , 25. How many cartons of milk should they order if there
are 399 students eating lunch today?
158 cartons of milk
Define variables and create an equation to solve the following questions.
7. At the Charleston Bowling Lanes, it costs $2 to rent shoes plus $1.50 per game of bowling. How many games
would you be able to bowl for $11?
' #+'$1,#-$
1; ' +,+'$1,#-$
1
' 1.50' 2; 6 games
8. You have already read 173 pages in the first book of the Twilight series. If you read about 65 pages every 2
nights, how long will it take you to finish the book that is 498 pages long?
#+/',C1$/'; # #+#$'1,C1$
D6
# 173; 10 days
9. To make the perfect pizza, there should be 4 pieces of pepperoni for every 3 slices of mushrooms. If you put
24 pieces of pepperoni, how many mushroom slices should you use?
#+.,C++,-/1,; # #+#1##1C+/
0
# ; 18 slices of mushrooms
10. The recipe for iced coffee at Starbucks suggests 2 parts milk for every 3 parts coffee. If a venti (the largest
size) requires 12 ounces of coffee, how many ounces of milk should be added?
+.1,++11; +.1,+/-E
; 8 ounces of milk
11. Your parents put a down payment on your car, but they are requiring you to pay the monthly payment of
$85. If you will have to pay a total of $2125 for the car, how long will it take you to pay it off?
#++,; 1&#$/+<$C,$C-+$
85; 25 months
12. The local humane society receives $45 for every dog they give up for adoption. If they spent $920 on
supplies, how much profit will they make if they have 24 dogs to give up for adoption?
#++',$+#1; # $+.+#C+/
# 45 920; $160 in profit
13. John has the sequence 0, 5, 10, 15, 20, 25 … What is the 15th term in the sequence?
1C#/,1F.11; G$-.1+1HI 1C
5; 75 is the 15th term
14. Joe has the sequence 9, 7, 5, 3, 1, 1 … What is the 10th term in the sequence?
1C#/,1F.11; G$-.1+1HI 1C
2 9; 11 is the 10th term
15. Jill has the sequence 3, 3.5, 4, 4.5, 5, 5.5, 6 … What is the 20th term in the sequence?
1C#/,1F.11; G$-.1+1HI 1C
0.5 3; 13 is the 20th term
16. Jane has the sequence 5, 4.25, 3.5, 2.75, 2, 1.25 … What is the 10th term in the sequence?
1C#/,1F.11; G$-.1+1HI 1C
0.75 5; 2.5 is the 10th term
Answer the following questions comparing linear function equations and descriptions.
Dr. Kal is studying how age and gender affect calorie expenditure. Here is the information about the number of
calories burned based on the number of miles walked in a day.
Paul (25)
Burns 1390 calories plus 1040 calories from walking 10
miles
Ishmael (58)
Burns 1305 calories plus 220 calories from walking 2
miles
Jerika (31)
Calorie expenditure is based on the equation =
98 + 1225
Pamela (62)
Calorie expenditure is based on the equation =
J6
+ 1189
17. Who burns the most calories per mile, and how do you know?
KLM
Ishmael 110
(list rates of calorie burning)
NOMP
18. Who burns the least calories per mile, and how do you know?
KLM
Jerika 98 NOMP (list rates of calorie burning)
19. Who burns the most calories without walking, and how do you know?
Paul 1390$20. How far would each person have to walk (to the nearest hundredth) to burn 2000 calories?
Paul: 5.87/-1,
Ishmael: 6.32/-1,
Jerika: 7.91/-1,
Pamela: 7.91/-1,
21. If each person walks 2 miles, who burns the most calories for that day?
Paul
22. If each person walks 10 miles, who burns the most calories for that day?
Paul
Answer the following questions comparing linear function equations and descriptions.
You are deciding which gas company to choose as you travel across the country on a long vacation with your
family. Here is the information about the cost for gallons of gas ' for each company.
Gas Up
Automart
Charges $4.01 for each gallon of gas
Charges $81 for 20 gallons of gas
The Fuel Shop
Cost is modeled by the equation = 4.03'
Full Tank
Cost is modeled by the equation = 4.10'
23. Which company charges the most per gallon of gas? How do you know?
Full Tank at $4.10
24. Which company charges the least per gallon of gas? How do you know?
Gas Up at $4.01
25. How much would each company charge you for 12 gallons of gas? Which is the cheapest?
Gas Up: $48.12
Automart: $48.60
The Fuel Shop: $48.36
Full Tank: $49.20
Gas Up is the cheapest
Lesson 2.3B
Use the given graph to solve the linear questions.
2. How much would it cost for four apples?
$3
Cost in Dollars
Cost in Dollars
1. How much will it cost for ten months of internet
service? $140
Apples
3. How many cups of butter should you use if you
use 1 cup of sugar? 0.75 cups
4. How many days will it take to get to page 200 in
the book? 4 days
Pages Read
Cups of Sugar
Months
Cups of Butter
6. How many miles can you travel if you have four
gallons of gas left in your tank? 100 miles
Miles Traveled
Money in Savings
5. How much money will you have saved after 6
months? $240
Days
Months
Gallons of Gas
Create an equation for the following linear graphs.
8. Number of elves 1 for Santa’s helpers 5
1 3
ElvesU
Pints of Paint )
7. Number of pints of paint # needed for a certain
number of square feet , # = 6 , + 1
Santa’s Helpers S
Square Feet Q
10. Cost of an order depending on the number
of shirts , purchased
5, 10
Saxophones Q
Cost in Dollars T
9. Number of saxophones , compared to the
number of flutes in an orchestra
2
, 3
Shirts Purchased Q
Flutes 12. Number of beats & per minute in a hiphop song
& 125
Height in feet S
Beats W
11. A tree’s height based on the number of
years since being transplanted
1
5
4
Minutes V
Years R
Answer the following questions comparing linear function equations, graphs and descriptions.
Various golf ball manufacturers offer deals for packs of golf balls. Here is the information about the total cost for golf balls ' including shipping costs.
Nike
Callaway
6
Charges a fee of $10 for shipping and $5 for 3 golf balls Cost is modeled by the equation = ' + 5
Titleist
Cost T
Cost T
Top-Flight
Golf Balls Y
Golf Balls Y
13. Which manufacturer has the cheapest cost per golf ball, and how do you know?
Callaway and Top-Flight tie at X $1.67 per ball (Titleist $2 per ball and Nike $2.50 per ball)
14. Which manufacturer has the cheapest shipping fee, and how do you know?
Titleist $0 shipping, it’s the -intercept or initial value
15. How many golf balls could you buy at each company for $20? Which manufacturer would give you the most
golf balls for that amount of money?
Cal: 6 golf balls
Nike: 6 golf balls
Titleist: 10 golf balls
Top-Flight: 9 golf balls
Titleist
16. How many golf balls could you buy at each company for $200? Which manufacture would give you the most
golf balls for that amount of money?
Cal: 114 golf balls
Nike: 78 golf balls
Titleist: 100 golf balls
Top-Flight: 117 golf balls
Top-Flight
17. Which manufacturer would be the cheapest if you wanted to buy 6 golf balls?
Titleist $12
18. Which manufacturer would be the cheapest if you wanted to buy 30 golf balls?
Top-Flight $55
Answer the following questions comparing linear function equations, graphs and descriptions.
Scientists are studying how location affects the speed of a bottlenose dolphin. Here is the information about the
distance in kilometers a dolphin traveled in terms of time in hours.
Dolphin in Mediterranean Sea
6
Distance is modeled by the equation = 0 Dolphin in Indian Ocean
Dolphin in North Atlantic Ocean
Distance Z
Distance Z
Dolphin in Gulf of Mexico
Swims 11 kilometers in 2 hours
Time (
Time (
19. Which location has the fastest dolphin?
Med Sea 8.75E#
20. Which location has the slowest dolphin?
Gulf of Mex 5.5E#
21. How far could each dolphin travel in 4 hours? Which location has the dolphin that went the farthest?
Gulf: 22E
Med Sea: 35E
Indian: 24E North Atl: 32E, Med Sea farthest
22. How long would it take each dolphin to swim 100 kilometers? Which location has the dolphin that finished in
the shortest amount of time?
Gulf: X 18.2+.C,
Med Sea: X 11.4+.C,
Indian: X 16.7+.C,
North Atl: 12.5+.C,
Med Sea fastest
Lesson 2.3C
Create an equation for the following tables.
1. The total cost for miles traveled in a taxi.
2. The money earned in a number of weeks <.
<
2
$4.50
4
$6
6
8
$7.50
$9
0.75 3
10
$10.50
3. The distance traveled in time in hours ℎ.
ℎ
2
14
3
21
4
5
28
35
7
6
42
2
$10
4
$20
6
8
$30
$40
5<
10
$50
4. The amount of profit # of a stand selling lemon
shake-ups -.
#
250
$50
300
$200
350
400
$350 $500
# 3- 700
450
$650
5. The total weight of an aquarium $ holding
gallons ' of water.
6. The number of dogs to herd cattle .
'
$
100
930
110
120
130
1015 1100 1185
$ 8.5' 80
140
1270
9
3
15
5
21
7
= 27
9
33
11
Use the given tables to solve the linear questions.
7. How much would it cost for 15 gallons of gas
'?
'
4
$14
6
8
$21
$28
$52.50
10
$35
12
$42
9. How much would it cost to buy 13 shirts ,
at Kohl’s?
,
2
$10
4
6
$30
$50
$120
8
$70
10
$90
11. How many cups of cheese would you need
for an 32-inch pizza #?
#
8
2
12
16
3
4
8.#,
20
5
24
6
8. How many minutes would it take for a pot of
water to reach a temperature of 210>?
1
85
2
3
110
135
6
4
160
5
185
10. How many songs , could your purchase for
$45 ?
,
4
$6
6
8
$9
$12
30,+',
10
$15
12
$18
12. How much profit # would Harry’s Hot Dogs
make if they sold 400 hot dogs in a month?
#
200
100
225
250
150
200
# $500
275
250
300
300
Answer the following questions comparing linear function equations, graphs, tables and descriptions.
Your neighborhood friends have decided to have a running race down the street. Here is the information about the
distance (including a head start in some cases) in terms of time in seconds.
Mitchell
Kyra
Runs 5 meters in 2 seconds and has a 10 meter head
[
Distance is modeled by the equation = + 3
start
Gloria
Hashim
Distance Z
20
77
22
84
Time (
13. Which runner has the fastest pace, and how do you know?
Kyra at X 4.5 meters per second (list other speeds)
14. Which runner has the biggest head start, and how do you know?
Mitchell at 10 meters (show work of getting initial values)
15. How far could each runner go in 4 seconds? Who would go the farthest?
Mitchell: 20
Kyra: 21
Gloria: 21
Hashim: 21
Three-way tie with Kyra, Gloria and Hashim
16. How far could each runner go in 10 seconds? Who would go the farthest?
Mitchell: 35
Kyra: 48
Gloria: 45
Hashim: 42
Kyra would go the farthest
17. Who would win the race if the race was 15 meters long?
Mitchell would win with a time of 2 seconds
18. Who would win the race if the race was 50 meters long?
Kyra would win with a time of about 10.4 seconds
24
91
26
98
28
105
Answer the following questions comparing linear function equations, graphs, tables and descriptions.
Your family is deciding which activity to participate in while on your vacation in San Diego. Here is the information
about the cost for admission for all of your family members .
City Tour
Charges $30 per family member
San Diego Zoo
?6
Cost is modeled by the equation = SeaWorld
Kayaking
2
65
4
130
6
195
8
260
10
325
Cost T
Family Members 19. Which activity is the cheapest per family member, and how do you know?
City tour at $30 per family member (list other costs per person)
20. Which activity is the most expensive per family member, and how do you know?
SeaWorld at $43.75 per family member (list other costs per person)
21. How many people could you bring to each activity if you budgeted $400? Which activity allows you to bring
the most people for that amount of money?
City Tour: 13 people
SD Zoo: 10 people
SeaWorld: 9 people
Kayak: 12 people
City tour allows most people (note you have to always round down since you can’t pay for a partial person)
22. How much would it cost at each activity to bring a family of 4? Which activity is the cheapest for that many
people?
City Tour: $120
SD Zoo: $150
SeaWorld: $175
Kayak: $130 people
City tour allows most people
Lesson 2.
2. 4
Solve each equation by using the distributive property, combining like terms, and eliminating the variable on
one side of the equation.
1. 2
+ 3 + 4 = 5
+ 10
= −1
2. 2# + 4# − 3 = 2# + 1
3. 8E + 5 + 2E = 23 + E
E=2
4. 4C + C + 14 = 5C − C + 1 − 3
C = −8
5. 2 + 3 = 2 − 3 + 2 + 6
=0
6. 4 − 1 + 2 = 2 + 2
=2
7. −5 + 2 = 3 + 2
=
9. 10$ + 1 = 2$ + 2 − 2
$ = −1
10. 5 − 3 + 7 = 3 − 1
=8
11. 5 − 25 + 2 = 2
=5
12. 42 + 1 + = 3 + 2
=
F = −2
14. 41 − 2. = 2. + 2
.=0
\=
16. 6 − 3 + 26 = 5 + 8
= −7
17. 6 + 1 = 4 81 + 0 9 + 6 + 3
=2
18. 9 − + 3 = −2 + 1
=
19. −
− 4 + 3
= 4
+ 1
=0
20. −2] + 5 + 6 = 4] + 2
] = −2
13.
F
+ 2F + 5 = −4F + 1 + 1
15. 5\ − \ + 3 = \ + 3 + 1
2
[
0
8.
0
6
− 3 + 4 = + 7 − 3
#=1
=0
2
Write an equation for each situation and then solve by using the distributive property, combining like terms,
and eliminating the variable on one side of the equation.
21. Tao is making a 7 feet high door. If the height is 1 foot more than twice its width, what is its width?
3 11
22. Terikka bought three bags of popcorn at the concession and a drink for $1.50. If she paid $3.75 total, how
much was each bag of popcorn?
$0.75
23. Naphtali’s cell phone company charges $0.25 per text plus a $10 flat fee. Asher’s cell phone company
charges $0.10 per text plus a $25 flat fee. At how many texts are Naphtali and Asher paying exactly the same
amount?
100 1,
24. Stanley bought five packs of Yu-Gi-Oh cards, $7 worth of bubble gum, and then eight more packs of Yu-Gi-Oh
cards. Simon bought four packs of Yu-Gi-Oh cards, $10 worth of Cheetos, $12 worth of Mt. Dew, and then six
more packs of Yu-Gi-Oh cards. If they paid the same amount, how much was each pack of Yu-Gi-Oh cards?
$5
25. Toby sells his framed paintings for $20 each. Ishmael sells his paintings for $14 each and charges a flat fee of
$18 for framing. How many paintings need to be purchased for Toby and Ishmael to charge the same amount?
3 #$//',
26. The original price of Doritos is the same at both Wal-Mart and County Market. Jon found out that Wal-Mart
had Doritos on sale at $0.50 off per bag and bought four bags. Later that day, he found out that County Market
had Doritos on sale at $1 off per bag and bought six bags. If he paid the same amount at both stores, what was
the original price of Doritos?
$2
Lesson 2.5
Solve the following equations. Some equations will have a single answer, others will have no solution, and still
others will have infinite solutions.
1. 2 + 2 + 2 = 4 + 2
///1,+-./+,
2. 3 − 1 = 2 + 9
= 12
3. 2 + 8 = 2 + 4
///1,+-./+,
4. 2 − + 7 = + 3 + 4
///1,+-./+,
5. −2 + 1 = −2 + 5
+,+-./+
6. 4 + 2 + 2 = 3 − 7
= −3
7. 2 + 2 + 3 = 2 + 1 + 1
8. 4 − 1 = − 8
=
2
0
=
2
11. 42 + 1 = 5 + 3 + 9
12. 10 + = 56 + 2
+,+-./+
+,+-./+
13. 8 + 2 = 2 + 16
=0
1
9. + 2 + 7 = 3 − 7
=0
10. 3 − + 4 = 42 − 1
16.
2 − 4 + 2 = 13
+,+-./+
///1,+-./+,
6
2
14. 3 + + 4 = 4 − +,+-./+
15.
17. 12 + 2 − = 9 + 6
18. 4 + 1 = 22 + 3
=
0
+ 6 = 3 + 9
///1,+-./+,
+,+-./+
19. 4 + 3 − 4 = 8 8 + 19
///1,+-./+,
20. + 5 + 4 = 32 − 1
+,+-./+
21. 5 + 2 − 3 = 2 + 5
///1,+-./+,
22. 3 + 1 = 3 − 1 + 4
///1,+-./+,
23. 4 + 2 − 5 = 7 − 1
= −4
24. −2 + 1 = 2 − 1
=0
25. 2 + 5 = 2 + 5
+,+-./+
26. 23 + 3 = 32 + 2
///1,+-./+,
27. 2 + 1 − 4 = −2 − 3
=0
28. 4 + 1 = 42 − =
29. 3 + 7 + 1 = 25 + 1
+,+-./+
30. 6 + 1 + 5 = 13 − 2 + 6
///1,+-./+,
Create multi-step equations with the given number of solutions.
All answers will vary.
31. A single solution
32. Infinite solutions
33. No solution
34. Infinite solutions
35. No solution
36. A single solution
37. No solution
38. A single solution
39. Infinite solutions
40. A single solution
41. Infinite solutions
42. No solution
Lesson 2.6
Find the inverse function for each of the following.
1. = + 3
2. = − + 4
3. = 2 + 3
' = 2 − 6
' =
4. = −3
' = − 5. = −3 + 5
6
' = − +
6. = 2 − 6
' = + 3
− +6
' = −
7. = − 5
8. = − − 2
9. = 2 − 7
' = − − 3
' = + 10. = 2
' = 11. = −3 − 6
' = − − 2
12. = + 4
' = − 4
' = 2 + 10
?
Decide if the given functions are inverse functions or not. Explain why or why not.
Explanations may vary
13. = 2 + 1
14. = − + 4
15. = −4
' = −2 − 1
Not inverse functions
' = −4 − 3
' = 2 − 4
Not inverse functions
'^_ = − + 4
16. = −2 − 3
17. = − 6
0
−
−
' =
Inverse functions
' = ' = − 0 Inverse functions
' = 18. = 2
0
' =
+6
Not inverse functions
'^_ = − 2
' = − Not inverse functions
'^_ = −
Answer the following questions about the function = `.
19. Is ' = the inverse function? Why or why not?
No, it is not the inverse function. Explanations may vary. Sample: ' = 20. Is ' = −3 the inverse function? Why or why not?
No, it is not the inverse function. Explanations may vary. Sample: '^_ = −3
21. Could have an inverse function? Why or why not?
No. Explanations may vary. Sample: There is no input
Lesson 2.7
Solve the following inequalities and graph the solution on a number line.
1. + 3 < 7
2. − + 4 ≤ 8
<8
≥ −6
3. 2 + 1 ≥ 11
4. − − 2 > −2
≥5
<0
5. − 6 < 2
6. 4 − 11 ≤ −3
> −5
≤2
7. 2 + 3 ≥ −13
8. − − 2 > −5
≥ −8
<6
Write and solve an inequality for each problem. Graph your solution on the number line.
9. Your middle school band is having a fundraiser selling boxes of Krispy Kreme donuts in order to purchase new
marching uniforms. They spent $3,500 advertising their fundraiser and make $1.75 per box sold. How many
boxes do they need to sell in order to at least break even?
1.75& − 3500 ≥ 0
& ≥ 2000
1900
2000
2100
10. The gymnasium can legally hold 1,250 people. During graduation, they set up rows of 15 chairs and have 50
chairs set aside for the faculty. How many rows could they put up in the gym?
15C + 50 ≤ 1250
C ≤ 80
79 80
81
11. Every study session at home should be around 20 minutes long. You know that you will spend class time
studying totaling 2 hours exactly. How many study sessions at home should you have if you want to spend at
least 5 hours studying?
1
,+2≥5
3
,≥9
8
9
10
12. For every 10 box tops, the school library gets $1 to buy new books for you to read. The school spends $200
on prizes for the box top competition. How many box tops need to be brought in if the library wants to purchase
$1,200 of new books?
1
& − 200 ≥ 1200
10
& ≥ 14,000
13,500
14,000 14,500
Graph the solution set to each two variable inequality on the coordinate plane provided.
13. < 2 1
14. 4 4
15. a 2 1
16. 5 4
17. 4 3 7
18. a 2
0
19. 2 3 4
20. 3 2
4 4
21. a 1
22. 5 1
23. 3 2
4 8
24.
2
a 6
ReviewUnit2:LinearFunctionsKEY
Please do not use a calculator. No calculator necessary.
Define variables and create an equation to model each of the following situations.
2. You have $4000 in your bank account, and
you pay $450 for every 12 months of cell
phone service.
1 = dollars in possession
1 = ears of corn sold
1 41 22
$ = amount in bank account
= number of months of payment
$ 37.50 4000
3.
4.
Cost in Dollars
1. You start the day with $22 in your pocket and then
sell ears of corn for $4 each.
Gallons of Gas
2 5
' = cost in dollars
' = gallons of gas
' 5'
5.
Number of
shirts
purchased
Amount of
money spent
6.
2
4
6
8
10
$36
$57
$78
$99
$120
Number of
songs
downloaded
Cost
5
6
7
8
9
$5.75
$6.90
$8.05
$9.20
$10.35
= number of shirts purchased
$ = amount of money spent
$ 10.5 15
= number of songs downloaded
= cost
1.15
7. 4, 1.5, 1, 3.5, 6, 8.5 …
= term number in the sequence
= value of the HI term
2.5 4
8. 11, 7, 3, 1, 5, 9 …
= term number in the sequence
= value of the HI term
4 11
Create a graph representation of the following linear functions.
9. There are 2 teachers for every 10 students
on the field trip.
11. 2
10. You owe your parents $10 for the dish you
broke. You earn $2 every 3 weeks in
allowance.
12. 3
Describe the transformation that takes for each function as compared to the function = ! + ".
13. + 3
Translated up 3 units
14. 3
Stretched three times as close to the -axis
15. 3 ∗ Stretched three times as far away
from the -axis
16. 3
Translated left 3 units
Identify the rate of change and initial value in each function, describe the rate of change and initial value in
context, and then give the equation of the line if necessary.
17. The function relating the cost of framing to how many inches of frame around a picture / is shown by
the following graph:
0
Rate of Change:___ _______
Total cost
Initial Value:____6_________
Independent Variable:_/____
Dependent Variable:_______
Contextual
Description of
Rate of Change
Contextual
Description of
Initial Value
It costs $1 for every
4 inches of frame.
There is an initial
fee of $6 no matter
what.
EQ of Line:__ 0 / 6____
Inches of frame
18. The amount of money in dollars a mailman gets paid # to deliver mail to houses is modeled by the
following function: # 4 125.
Rate of Change:___4_______
Contextual Description of
Rate of Change
Contextual Description of
Initial Value
The mailman gets paid $4
per house.
The mailman gets paid $125
no matter what.
Initial Value:____125_________
Independent Variable:_____
Dependent Variable:_#_____
19. Imagine you’re spending winter break visiting your relatives in New York. It costs $1200 for the plane ticket
and $300 per night for the hotel. Think of the function that demonstrates the cost based on the number of
nights you spend.
Rate of Change:__300________
Initial Value:___1200__________
Independent Variable:_____
Dependent Variable:______
EQ of Line:___ 300 1200__
Contextual Description of
Rate of Change
Contextual Description of
Initial Value
The cost increases by $300
per night.
There is an initial cost of
$1200 no matter what
because of the plane tickets.
Write and solve an equation for the following situations.
20. Assuming each car has 4 tires, how many cars can you service if you have 120 tires?
30 cars
21. It costs $36 to enter a carnival plus $2 for each ticket to play games. How many games can you play if you
have $50 to spend?
7 games
22. A recipe for lasagna calls for cup cheese for every layer plus 1 cup of cheese on top. How many cups of
cheese would you need if you wanted to make 4 layers?
3 cups
Answer the questions on the following page comparing proportional function equations and descriptions.
Carla’s Cookies is looking for a new machine to make their cookies. Here is the information about the amount
of cookies made () in terms of time () in minutes and power consumption (#) in watts of electricity in terms
of time () in minutes for the machines.
Machine A:
Cookies made is modeled by the equation = 23
Power consumption is modeled by the equation # 3.5 4
Machine B:
Cookies made is modeled in the following table
10
200
20
400
30
600
40
800
50
1000
Power consumption is modeled in the following table
#
20
27
30
38
Time in minutes (
Machine D:
40
49
50
60
Power consumption graph
Power in watts )
Cookies graph
Cookies Made T
Machine C:
10
16
Time in minutes (
Makes approximately 690 cookies in 30 minutes
Consumes approximately 90 watts in 30 minutes plus an initial 3 watts to power up the machine
23. Which machine makes cookies the fastest and how do you know?
Machine C because it makes 25 cookies per minute
24. Which machine makes cookies the slowest and how do you know?
Machine B because it makes 20 cookies per minute
25. Which machine uses the most power per minute and how do you know?
Machine A because it uses 3.5 watts per minute
26. Which machine uses the least power per minute and how do you know?
Machine B because it uses 1.1 watts per minute
27. Which machine uses the least power to turn on (initially) and how do you know?
Machines C and D because they use 3 watts to turn on
28. Which machine would use the least total power if it ran for 30 minutes?
Machine B because it will use 38 watts in 30 minutes
29. Which machine would use the least total power if it ran for 10 minutes?
Machine B because it will use 16 watts in 10 minutes
Solve the following equations for the given variable. There may be a single solution, infinite
solutions, or no solutions.
6
30. 2 + − 8 + 2 = 3
=2
31. 3 + 4 − 2 = 9
= −3
32. 32
+ 5 − 6 = 4
+ 10
= 0.5
33. 2& + 2 = & + 6
&=0
34. 5' + 6 − 2 = 4' + 4 + '
///1,+-./+,
35. 4
+ 9 − = 3
+ 3
///1,+-./+,
36. 5 − + 2 = 4 + 8
= −1
37. 2 + 4] − 5 = 10]
] = −0.5
Find the inverse function of the given function.
38. = − 8
6
' 6
20
39. = −3 6
' = − + 2
Solve the following inequalities and graph the solutions on the number line.
40.
0
+534
41. −3 2 4 10
5 −4
3 4
−5 −4 −3
−5 −4 −3
Graph the following inequalities on the coordinate plane.
42. < − 3
43. 5 −4 1