Pre-Test Unit 2: Linear Functions KEY

Transcription

1 Pre-Test Unit 2: Linear Functions KEY 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 ( ) = Time racing in seconds Distance traveled in meters = input = output = , 1.5, 1, 0.5, 0, 0.5, = 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. ℎ( ) = 2 + 5

2 Describe the transformation that takes for each function as compared to the function () = +. (4 pts; partial credit at teacher discretion) 7. () (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) 9. The function relating the cost in dollars of entering a carnival, (), to how many tickets you buy,, is shown by the following graph: : 0.5 Total cost ROC in Context:_It costs $1 for two tickets or $0.50 per ticket : $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 ROC in Context: The gets $300 per acre left fallow : 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? = 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? = = $1.25

3 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. Rocket A: Power consumption is modeled by the equation = 1.6 Rocket B: Power consumption is modeled in the following table Rocket C: Power consumption graph Power in kw () Rocket D: Time in Hours () 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) = ( + 2) = 22 = 5 = 4

4 = ( + 2) = = = ( + 2) = Find the inverse function of the given function. (4 pts; 2 pts for work, 2 pts for answer) 21. f(x) = x + 4 f (x) = 2 3 x 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. x 2 < x 2 8 x < 8 x 5 Graph the following inequalities on the coordinate plane. (4 pts; 2 pts for line placement and type, 2 pts for shading) 24. y < x y 3x 7

5 Lesson 2.1 Unit 2 Homework Answer Key 23 Graph the following linear equations using slope-intercept form. 1. = = = = 7 5. = = = 2 8. = 1 9. = 4

6 = = = = = = = = = 9

7 Use the given functions to describe the listed transformations. Then write the equation of the transformed function. () = 3 2 () = h() = (2) () 21. () 2 Stretched twice as close to the -axis Stretched 2 x far away from -axis Translated down 2 units (2) = () = 6 4 () 2 = ( + 2) 23. ( ) 24. () Translated left 2 units Reflected across -axis Half as far away from the -axis ( + 2) = ( ) = () = () ( 5) 27. ( ) Translated up 5 units Translated right 5 units Stretched half as close to the -axis () + 5 = ( 5) = = () 29. h() h( + 6) Reflected across -axis Translated down 4 units No translation Stretched 3 times as far away since it is a horizontal line from the -axis 3 () = 6 12 h() 4 = 1 h( + 6) = h(2) h() 33. () 3 No translation Stretched twice as far away Translated down 3 units since it is a horizontal line from the -axis h(2) = 5 2 h() = 10 () 3 = 3 5

8 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: = Dependent Variable: Independent Variable: : 5 : 2 EQ of Line: = The rocket travels 5 meters per second, Before the rocket launches (when time is 0), it is two meters off the ground. 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: Cost ($) Dependent Variable: Independent Variable: : : 2 Contextual Description of The taxi charges one dollar per two miles traveled. Contextual Description of A passenger is charged $2 when 0 miles are traveled. 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 (h). Dependent Variable: Independent Variable: h : 2.25 : 105 EQ of Line:_ = 2.25h 105 _ Planet Wiener makes $2.25 for every hotdog sold. Planet Wiener spends $105 on food and supplies.

9 Profit 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: = Dependent Variable: Independent Variable: : 8.5 : 20 EQ of Line: = 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 Dependent Variable: Independent Variable: Description of Description of Number of glasses sold Each gallon of water weighs 8.5 pounds. : : 3 EQ of Line: = 3 The tank weighs 20 pounds without water in it. The sellers make of a dollar ($0.75) per glass of lemonade sold. If the sellers sell 0 glasses of lemonade, they will have lost $3 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 (h) in terms of the time it has been burning (). Dependent Variable: h Independent Variable: : : 5 The candle burns 1 inch every 2 hours. The candle starts at a height of 5 inches. EQ of Line: h = + 5

10 7. The cost () to stay in a 4 star hotel each night () is modeled by the following function: = Dependent Variable: Independent Variable: : 104 : 15 EQ of Line: = It costs $104 each night There is a $15 fee. 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 Dependent Variable: Independent Variable: Description of Description of Days : 25 : 0 EQ of Line: = 25 It costs $25 per day to attend the sports clinic. There is no initial value. 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 (). Dependent Variable: Independent Variable: : 40 : 10 EQ of Line: = It costs $40 per night. There is a $10 bathing fee.

11 10. The number of gallons of gas in your 15 gallon gas tank () based on the number of miles traveled () is modeled y the following function: = Dependent Variable: Independent Variable: : : 12 EQ of Line: = + 12_ The car uses 1 gallons of gas every 25 miles. 12 gallons of gas are in the tank to begin with. 11. The number of pizzas ordered for 8 th grade night () based on the number of students () is shown by the following graph: Number of pizzas Number of students Dependent Contextual Variable: Contextual Description of Description of Independent Variable: : a pizza was 2 pizzas are ordered ordered for each when there are 0 Initial student, Value: 2 or 1 pizza students. was ordered for EQ of Line: = + 2 every 4 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 (). Dependent Variable: Independent Variable: : 0.30 : 5.50 EQ of Line: = 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.

12 Grade earned 13. An author wrote an 876-page book. The amount of profit () based on the number books sold () is modeled by the following function: = Dependent Variable: Independent Variable: : 7 : 1050 EQ of Line: = There is a $7 profit for each book sold. : 10 : 40 EQ of Line: = 10h + 40 There is a $1050 profit when no books are sold. 14. The average grade earned on the Unit 3 test () based on the number of hours of studying (h) is modeled by the following graph: Contextual Contextual Dependent Variable: Independent Variable: h Description of Description of A student earns an extra 10% for every hour of studying. A student earns 40% when he/she studies for 0 hours. Hours of studying 15. Kiley invited 32 people to her 13 th 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 (). Dependent Variable: Independent Variable: : 2 : 40 EQ of Line: = It costs $2 per friend to bowl. It costs $40 if 0 friends bowl.

13 Temperature 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. Dependent Variable: Independent Variable: : 30 : 0 EQ of Line: = 30 Minutes You earn $30 for each yard you mow. : 5 : 40 EQ of Line: = You have $0 in your account before you mow any yards. 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 Dependent Variable: Independent Variable: Description of Description of The temperature increases 5 every minute it s in the oven. The chicken breast is 40 before it goes in the oven. 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. Dependent Variable: Independent Variable: : 3 : 2 EQ of Line: = There are 3 lifeguards for each slide. There are 2 lifeguards at the wave pool

14 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 (h) would be based on the equation h = 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 = 525. How much profit would you make if you were scheduled to mow 48 yards the first summer? $ 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 = How many cartons of milk should they order if there are 399 students eating lunch today? 158 cartons of milk

15 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? = # ; () = () = ; 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? = # h ; () = # () = + 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? = # h ; () = # () = ; 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? = ; () = () = ; 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? = # h; () = () = 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? = # ; () = () = ; $160 in profit 13. John has the sequence 0, 5, 10, 15, 20, 25 What is the 15 th term in the sequence? = # ; () = h () = 5; 75 is the 15 th term 14. Joe has the sequence 9, 7, 5, 3, 1, 1 What is the 10 th term in the sequence? = # ; () = h () = 2 + 9; 11 is the 10 th term 15. Jill has the sequence 3, 3.5, 4, 4.5, 5, 5.5, 6 What is the 20 th term in the sequence? = # ; () = h () = ; 13 is the 20 th term 16. Jane has the sequence 5, 4.25, 3.5, 2.75, 2, 1.25 What is the 10 th term in the sequence? = # ; () = h () = ; 2.5 is the 10 th term

16 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 = Pamela (62) Calorie expenditure is based on the equation = Who burns the most calories per mile, and how do you know? Ishmael 110 (list rates of calorie burning) 18. Who burns the least calories per mile, and how do you know? Jerika 98 (list rates of calorie burning) 19. Who burns the most calories without walking, and how do you know? Paul How far would each person have to walk (to the nearest hundredth) to burn 2000 calories? Paul: 5.87 Ishmael: 6.32 Jerika: 7.91 Pamela: 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 = Which company charges the most per gallon of gas? How do you know? Full Tank at $ Which company charges the least per gallon of gas? How do you know? Gas Up at $ 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

17 Lesson 2.3B Use the given graph to solve the linear questions. 1. How much will it cost for ten months of internet service? $ How much would it cost for four apples? $3 Cost in Dollars Months 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 5. How much money will you have saved after 6 months? $ How many miles can you travel if you have four gallons of gas left in your tank? 100 miles Money in Savings Pages Read Cost in Dollars Apples Cups of Butter Days Miles Traveled Cups of Sugar Months Gallons of Gas

18 Create an equation for the following linear graphs. 7. Number of pints of paint () needed for a certain number of square feet () = Number of elves () for Santa s helpers (h) = 5 3 h Pints of Paint () Square Feet () 9. Number of saxophones () compared to the number of flutes () in an orchestra = Cost () of an order depending on the number of shirts () purchased = A tree s height (h) based on the number of years () since being transplanted h = Number of beats () per minute () in a hiphop song = 125 Height in feet () Cost in Dollars () Elves() Santa s Helpers () Flutes () Shirts Purchased () Beats () Saxophones () Minutes () Years ()

19 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. Callaway Nike Charges a fee of $10 for shipping and $5 for 3 golf Cost is modeled by the equation = balls + 5 Titleist Top-Flight Cost () Cost () Golf Balls () Golf Balls () 13. Which manufacturer has the cheapest cost per golf ball, and how do you know? Callaway and Top-Flight tie at $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 $ Which manufacturer would be the cheapest if you wanted to buy 30 golf balls? Top-Flight $55

20 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 Gulf of Mexico Swims 11 kilometers in 2 hours Dolphin in Indian Ocean Dolphin in Mediterranean Sea Distance is modeled by the equation = Dolphin in North Atlantic Ocean Distance () Distance () Time () Time () 19. Which location has the fastest dolphin? Med Sea 8.75 h 20. Which location has the slowest dolphin? Gulf of Mex 5.5 h 21. How far could each dolphin travel in 4 hours? Which location has the dolphin that went the farthest? Gulf: 22 Med Sea: 35 Indian: 24 North Atl: 32, 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: 18.2 h Med Sea: 11.4 h Indian: 16.7 h North Atl: 12.5 h Med Sea fastest

21 Lesson 2.3C Create an equation for the following tables. 1. The total cost () for miles () traveled in a taxi $4.50 $6 $7.50 $9 $10.50 = The distance traveled () in time in hours (h). h = 7h 5. The total weight of an aquarium () holding gallons () of water = The money earned () in a number of weeks () $10 $20 $30 $40 $50 = 5 4. The amount of profit () of a stand selling lemon shake-ups () $50 $200 $350 $500 $650 = The number of dogs () to herd cattle () = Use the given tables to solve the linear questions. 7. How much would it cost () for 15 gallons of gas ()? $14 $21 $28 $35 $42 $ How many minutes () would it take for a pot of water to reach a temperature () of 210? = 6 9. How much would it cost () to buy 13 shirts () at Kohl s? $10 $30 $50 $70 $90 = $ How many songs () could your purchase for $45 ()? $6 $9 $12 $15 $ How many cups of cheese () would you need for an 32-inch pizza ()? How much profit () would Harry s Hot Dogs make if they sold 400 hot dogs (h) in a month? h = $500

22 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 = start + 3 Gloria Hashim Distance () Time () 13. Which runner has the fastest pace, and how do you know? Kyra at 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

23 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 SeaWorld San Diego Zoo Cost is modeled by the equation = Kayaking Cost () 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

24 Lesson 2.4 Solve each equation by using the distributive property, combining like terms, and eliminating the variable on one side of the equation = = = = = 23 + = = = = 2 (3 + 2) + 6 = ( 1) + 2 = 2( + 2) = ( + 2) = = = = ( + 1) = 2( + 2) 2 = = 3 1 = = 2 = (2 + 1) + = 3( + 2) = ( + 5) = 4( + 1) + 1 = (1 2) = 2( + 2) = = = = 5( + 8) = ( + 1) = = = 2( + 1) = 19. ( 4) + 3 = 4( + 1) = ( + 5) + 6 = 4( + 2) = 2

25 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? 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? $ 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? 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? 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

26 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( + 4) = = ( + 1) = = 3 7 = ( + 2) + 3 = 2( + 1) ( 1) = ( 8) = 3 7 = = = 4(2 1) 11. 4(2 + 1) = = 5( + 2) = 13. 8( + 2) = = (2 + 6) = = (2 4) + 2 = = = 2(2 + 3) = 19. 4( + 3) 4 = = 3(2 1) 21. 5( + 2) 3 = 2( + 5) = 3( 1) = ( + 1) = 2( 1) = 4 = ( + 5) = (3 + 3) = 3(2 + 2) = 2 3 = ( + 1) = 4(2 ) = 2(5 + 1) 30. 6( + 1) + 5 = =

27 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

28 Lesson 2.6 Find the inverse function for each of the following. 1. () = () = () = () = 2 6 () = + 6 () = 4. () = 3 5. () = () = 2 6 () = () = + () = () = 5 8. () = 2 9. () = 2 7 () = () = 3 () = () = () = () = + 4 () = () = 2 () = 4 Decide if the given functions are inverse functions or not. Explain why or why not. Explanations may vary 13. () = () = () = 4 () = 2 1 () = 2 4 () = Not inverse functions Not inverse functions Inverse functions (()) = 4 3 () = + 4 (()) = 16. () = () = () = 2 () = () = + 6 () = Inverse functions Not inverse functions Not inverse functions (()) = () = 2 () = 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: () = Could () have an inverse function? Why or why not? No. Explanations may vary. Sample: There is no input

29 Lesson 2.7 Solve the following inequalities and graph the solution on a number line < < > 2 5 < 0 5. < > > 5 8 < 6

30 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? 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? 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? 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? ,000 13,500 14,000 14,500

31 Graph the solution set to each two variable inequality on the coordinate plane provided. 13. < > > + 2

32 < > > 6

33 Review Unit 2: Linear Functions KEY Please do not use a calculator. No calculator necessary. Define variables and create an equation to model each of the following situations. 1. You start the day with $22 in your pocket and then 2. You have $4000 in your bank account, and sell ears of corn for $4 each. you pay $450 for every 12 months of cell phone service. () = dollars in possession () = amount in bank account = ears of corn sold = number of months of payment () = () = Cost in Dollars Gallons of Gas () = 2 5 () = cost in dollars = gallons of gas () = Number of Number of shirts songs purchased downloaded Amount of $36 $57 $78 $99 $120 Cost $5.75 $6.90 $8.05 $9.20 $10.35 money spent = number of shirts purchased = number of songs downloaded () = amount of money spent () = cost () = () = , 1.5, 1, 3.5, 6, , 7, 3, 1, 5, 9 = term number in the sequence = term number in the sequence () = value of the term () = value of the term () = () =

34 Create a graph representation of the following linear functions. 9. There are 2 teachers for every 10 students 10. You owe your parents $10 for the dish you on the field trip. broke. You earn $2 every 3 weeks in allowance. 11. h() = h() = 3 Describe the transformation that takes for each function as compared to the function () = () (3) Translated up 3 units Stretched three times as close to the -axis () 16. ( + 3) Stretched three times as far away Translated left 3 units from the -axis

35 Total cost 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: Inches of frame Dependent Variable: Independent Variable: : : _6 EQ of Line: = + 6 Contextual Description of It costs $1 for every 4 inches of frame. Contextual Description of There is an initial fee of $6 no matter what. 18. The amount of money in dollars a mailman gets paid () to deliver mail to houses (h) is modeled by the following function: = 4h Dependent Variable: Independent Variable: _h : _4 : _125 The mailman gets paid $4 per house. Type equation here. The mailman gets paid $125 no matter what. 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. Dependent Variable: 300 Independent Variable: _1200_ : : EQ of Line: = The cost increases by $300 per night. There is an initial cost of $1200 no matter what because of the plane tickets.

36 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 = Machine B: Cookies made is modeled in the following table Power consumption is modeled in the following table Machine C: Cookies graph Power consumption graph Cookies Made () Power in watts () Time in minutes () Time in minutes () Machine D: Makes approximately 690 cookies in 30 minutes Consumes approximately 90 watts in 30 minutes plus an initial 3 watts to power up the machine

37 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 = ( + 4) 2 = 9 = 2 = (2 + 5) 6 = ( + 2) = ( + 6) = 0.5 = = = 3( + 3) ( + 2) = = 10 = 1 = 0.5

38 Find the inverse function of the given function. 38. f(x) = x f(x) = 3x + 6 g(x) = x + 20 g(x) = x + 2 Solve the following inequalities and graph the solutions on the number line. 40. x + 5 < x 2 10 x < 4 x Graph the following inequalities on the coordinate plane. 42. y < x y 4x + 1