1. first differences First differences are the differences between successive data points.

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1 Lesson.1 Skills Practice Name Date The Plane! Modeling Linear Situations Vocabular Define each term in our own words. 1. first differences First differences are the differences between successive data points.. solution The solution of a linear equation is an value that makes an open sentence true. 3. intersection point The intersection point is the point on the graph where one line crosses another. Problem Set Identif the independent and dependent quantities in each problem situation. Then write a function to represent the problem situation. 1. Nathan is riding his scooter to school at a rate of 6 miles per hour. The distance Nathan travels depends on the time. Distance, D, is the dependent quantit and time, t, is the independent quantit. D(t) 5 6t 01 Carnegie Learning. Sophia is walking to the mall at a rate of 3 miles per hour. The distance Sophia travels depends on the time. Distance, D, is the dependent quantit and time, t, is the independent quantit. D(t) 5 3t 3. Mario is stuffing envelopes with invitations to the school s Spring Carnival. He stuffs 5 envelopes each minute. The total number of envelopes Mario stuffs depends on the time. The total number of envelopes, E, is the dependent quantit and time, t, is the independent quantit. E(t) 5 5t Chapter Skills Practice 81

2 Lesson.1 Skills Practice page 4. Shanise plas on the varsit soccer team. She averages 4 goals per game. The total number of goals Shanise scores depends on the number of games she plas. The total number of goals scored, S, is the dependent quantit and the number of games plaed, g, is the independent quantit. S(g) 5 4g 5. The football booster club sells hot chocolate during the varsit football games. Each cup of hot chocolate costs $. The amount of mone the booster club earns depends on the number of cups sold. The amount of mone, M, is the dependent quantit and the number of cups sold, c, is the independent quantit. M(c) 5 c 6. The basketball booster club sells t-shirts at the varsit basketball games. Each t-shirt costs $1. The amount of mone the booster club earns depends on the number of t-shirts sold. The amount of mone, M, is the dependent quantit and the number of t-shirts sold, t, is the independent quantit. M(t) 5 1t Use each scenario to complete the table of values and calculate the unit rate of change. 7. Miguel is riding his bike to lacrosse practice at a rate of 7 miles per hour. Independent Quantit Dependent Quantit Quantit Time Distance Units hours miles (0.5, 3.5) and (1, 7) The unit rate of change is 7. Epression t 7t Carnegie Learning 14 8 Chapter Skills Practice

3 Lesson.1 Skills Practice page 3 Name Date 8. Jada is walking to school at a rate of miles per hour. Independent Quantit Dependent Quantit Quantit Time Distance Units hours miles (0.5, 0.5) and (0.5, 1) The unit rate of change is. Epression t t Noah is stuffing envelopes with invitations to the school s Harvest Festival. He stuffs 4 envelopes each minute. 01 Carnegie Learning Independent Quantit Dependent Quantit Quantit Time Number of Envelopes Units minutes envelopes Epression t 4t (5, 0) and (10, 40) The unit rate of change is Chapter Skills Practice 83

4 Lesson.1 Skills Practice page Terell plas on the varsit basketball team. He averages 1 points per game. Independent Quantit Dependent Quantit Quantit Number of games plaed Total number of points scored Units games points (3, 36) and (5, 60) The unit rate of change is 1. Epression g 1g The volleball boosters sell bags of popcorn during the varsit matches to raise mone for new uniforms. Each bag of popcorn costs $3. Quantit Independent Quantit Number of bags of popcorn sold Dependent Quantit Amount of mone raised Units bags dollars (5, 15) and (10, 30) The unit rate of change is 3. Epression b 3b Carnegie Learning Chapter Skills Practice

5 Lesson.1 Skills Practice page 5 Name Date 1. The football boosters sell hooded sweatshirts to raise mone for new equipment. Each sweatshirt costs $18. Quantit Independent Quantit Number of sweatshirts sold Dependent Quantit Amount of mone raised Units sweatshirts dollars (5, 90) and (10, 180) The unit rate of change is 18. Epression s 18s Identif the input value, the output value, and the rate of change for each function. 01 Carnegie Learning 13. Belinda is making greeting cards. She makes 4 cards per hour. The function C(t) 5 4t represents the total number of cards Belinda makes as a function of time. The input value is t. The output value is 4t. The rate of change is Owen is riding his bike to his friend s house at a rate of 6 miles per hour. The function D(t) 5 6t represents the distance Owen rides as a function of time. The input value is t. The output value is 6t. The rate of change is 6. Chapter Skills Practice 85

6 Lesson.1 Skills Practice page Rochelle is shopping for earrings. Each pair of earrings costs $15 dollars. The function C(e) 5 15e represents the total cost of the earrings as a function of the number of pairs of earrings Rochelle bus. The input value is e. The output value is 15e. The rate of change is Lavon is driving to visit a college campus. He is traveling 65 miles per hour. The function D(t) 5 65t represents the total distance he travels as a function of time. The input value is t. The output value is 65t. The rate of change is Kiana is selling coupon books to raise mone for her school. Each coupon book cost $35. The function M(b) 5 35b represents the total amount of mone raised as a function of the number of coupon books sold. The input value is b. The output value is 35b. The rate of change is Cisco mows lawns in his neighborhood to earn mone. He earns $16 for each lawn. The function A(m) 5 16m represents the total amount of mone earned as a function of the number of lawns mowed. The input value is m. The output value is 16m. The rate of change is Carnegie Learning 86 Chapter Skills Practice

7 Lesson.1 Skills Practice page 7 Name Date Solve each function for the given input value. The function A(t) = 7t represents the total amount of mone in dollars Carmen earns babsitting as a function of time in hours. 19. A(3) 5 A(3) 5 7(3) 5 1 Carmen earns $1 when she babsits for 3 hours. 0. A() 5 A() 5 7() 5 14 Carmen earns $14 when she babsits for hours. 1. A(5) 5 A(5) 5 7(5) 5 35 Carmen earns $35 when she babsits for 5 hours.. A(4.5) 5 A(4.5) 5 7(4.5) Carmen earns $31.50 when she babsits for 4.5 hours. 01 Carnegie Learning 3. A(3.5) 5 A(3.5) 5 7(3.5) Carmen earns $4.50 when she babsits for 3.5 hours. 4. A(6) 5 A(6) 5 7(6) 5 4 Carmen earns $4 when she babsits for 6 hours. Chapter Skills Practice 87

8 Lesson.1 Skills Practice page 8 Use the graph to determine the input value for each given output value. The function D(t) 5 40t represents the total distance traveled in miles as a function of time in hours. Distance (miles) Time (hours) D(t) D(t) 5 30 D(t) 5 40 D(t) D(t) 5 10 D(t) 5 80 t 5. D(t) D(t) 5 30 t 5 3 t D(t) D(t) t 5 6 t Carnegie Learning 9. D(t) D(t) t 5 t Chapter Skills Practice

9 Lesson. Skills Practice Name Date What Goes Up Must Come Down Analzing Linear Functions Problem Set Complete the table to represent each problem situation. 1. A hot air balloon cruising at 1000 feet begins to ascend. It ascends at a rate of 00 feet per minute. Independent Quantit Dependent Quantit Quantit Time Height Units minutes feet Carnegie Learning Epression t 00t Chapter Skills Practice 89

10 Lesson. Skills Practice page. A bathtub contains 10 gallons of water. The faucet is turned on and fills the tub at a rate of 5.5 gallons per minute. Independent Quantit Dependent Quantit Quantit Time Volume Units minutes gallons Epression t 5.5t A helicopter fling at 415 feet begins its descent. It descends at a rate of 550 feet per minute. Independent Quantit Dependent Quantit Quantit Time Height Units minutes feet Carnegie Learning Epression t 550t Chapter Skills Practice

11 Lesson. Skills Practice page 3 Name Date 4. A fish tank filled with 1 gallons of water is drained. The water drains at a rate of 1.5 gallons per minute. Independent Quantit Dependent Quantit Quantit Time Volume Units minutes gallons Epression t 1.5t A submarine is traveling at a depth of 300 feet. It begins ascending at a rate of 8 feet per minute. Independent Quantit Dependent Quantit Quantit Time Depth 01 Carnegie Learning Units minutes feet Epression t 8t 300 Chapter Skills Practice 91

12 Lesson. Skills Practice page 4 6. A free-diver is diving from the surface of the water at a rate of 15 feet per minute. Independent Quantit Dependent Quantit Quantit Time Depth Units minutes feet Epression t 15t Identif the input value, the output value, the -intercept, and the rate of change for each function. 7. A hot air balloon at 130 feet begins to ascend. It ascends at a rate of feet per minute. The function f(t) t represents the height of the balloon as it ascends. The input value is t, time in minutes. The output value is f(t), height in feet. The -intercept is 130. The rate of change is A backard pool contains 500 gallons of water. It is filled with additional water at a rate of 6 gallons per minute. The function f(t) 5 6t represents the volume of water in the pool as it is filled. The input value is t, time in minutes. The output value is f(t), volume in gallons. The -intercept is 500. The rate of change is A submarine is diving from the surface of the water at a rate of 17 feet per minute. The function f(t) 5 17t represents the depth of the submarine as it dives. The input value is t, time in minutes. The output value is f(t), depth in feet. The -intercept is 0. The rate of change is Carnegie Learning 9 Chapter Skills Practice

13 Lesson. Skills Practice page 5 Name Date 10. A helicopter fling at 3505 feet begins its descent. It descends at a rate of 470 feet per minute. The function f(t) 5 470t represents the height of the helicopter as it descends. The input value is t, time in minutes. The output value is f(t), height in feet. The -intercept is The rate of change is A bathtub contains 5 gallons of water. The faucet is turned on and water is added to the tub at a rate of 4.5 gallons per minute. The function f(t) 5 4.5t 1 5 represents the volume of water in the bathtub as it is filled. The input value is t, time in minutes. The output value is f(t), volume in gallons. The -intercept is 5. The rate of change is A free-diver is diving from the surface of the water at a rate of 8 feet per minute. The function f(t) 5 8t represents the depth of the diver. The input value is t, time in minutes. The output value is f(t), depth in feet. The -intercept is 0. The rate of change is 8. Sketch the line for the dependent value to estimate each intersection point. 13. f() when f() f() when f() Carnegie Learning Answers will var. Answers will var. f() 5 70 at 5 1 f() 5 75 at 5 10 Chapter Skills Practice 93

14 Lesson. Skills Practice page f() when f() f() when f() Answers will var. Answers will var. f() 5 7 at 5 6 f() 5 8 at f() when f() = f() when f() Answers will var. Answers will var. f() at 10 f() 5 40 at 8 01 Carnegie Learning 94 Chapter Skills Practice

15 Lesson. Skills Practice page 7 Name Date Substitute and solve for to determine the eact value of each intersection point. 19. f() when f() f() when f() 5 75 f() f() f() when f() 5 7. f() when f() 5 8 f() f() f() when f() f() when f() 5 40 f() f() Carnegie Learning Chapter Skills Practice 95

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17 Lesson.3 Skills Practice Name Date Scouting for Prizes! Modeling Linear Inequalities Vocabular Define the term in our own words. 1. solve an inequalit To solve an inequalit means to determine the values of the variable that make the inequalit true. Problem Set Carlos works at an electronics store selling computer equipment. He can earn a bonus if he sells $10,000 worth of computer equipment this month. So far this month, he has sold $4000 worth of computer equipment. He hopes to sell additional laptop computers for $800 each to reach his goal. The function f() represents Carlos s total sales as a function of the number of laptop computers he sells. 01 Carnegie Learning Total Sales (dollars) 18,000 16,000 14,000 1,000 10, Number of Laptop Computers Sold Chapter Skills Practice 97

18 Lesson.3 Skills Practice page Use the graph to write an equation or inequalit to determine the number of laptop computers Carlos would need to sell to earn each amount. 1. at least $10,000. less than $7000 Carlos would need to sell at least Carlos would need to sell fewer than 8 laptop computers. 4 laptop computers. $ 8, 4 3. less than $ at least $9000 Carlos would need to sell fewer than Carlos would need to sell at least 3 laptop computers. 7 laptop computers., 3 $ 7 5. more than $1, eactl $8000 Carlos would need to sell more than Carlos would need to sell eactl 10 laptop computers. 5 laptop computers Elena works at the ticket booth of a local plahouse. On the opening night of the pla, tickets are $10 each. The plahouse has alread sold $500 worth of tickets during a presale. The function f() represents the total sales as a function of tickets sold on opening night. Total Sales (dollars) Tickets Sold Opening Night 01 Carnegie Learning 98 Chapter Skills Practice

19 Lesson.3 Skills Practice page 3 Name Date Use the graph of the function to answer each question. Graph each solution on the number line. 7. How man tickets must Elena sell in order to make at least $1000? Elena must sell at least 50 tickets. $ How man tickets must Elena sell in order to make less than $800? Elena must sell fewer than 30 tickets., How man tickets must Elena sell in order to make at least $100? Elena must sell at least 70 tickets. $ How man tickets must Elena sell in order to make eactl $1400? Elena must sell eactl 90 tickets How man tickets must Elena sell in order to make less than $600? Elena must sell fewer than 10 tickets., Carnegie Learning How man tickets must Elena sell in order to make eactl $900? Elena must sell eactl 40 tickets Chapter Skills Practice 99

20 Lesson.3 Skills Practice page 4 Leon plas on the varsit basketball team. So far this season he has scored a total of 5 points. He scores an average of 13 points per game. The function f() represents the total number of points Leon will score this season. Write and solve an inequalit to answer each question. 13. How man more games must Leon pla in order to score at least 117 points? f() # # 13 5 # Leon must pla in 5 or more games to score at least 117 points. 14. How man more games must Leon pla in order to score fewer than 18 points? f() Leon must pla in fewer than 10 games to score fewer than 18 points. 15. How man more games must Leon pla in order to score more than 143 points? f() , , 13 7, Leon must pla in more than 7 games to score more than 143 points. 01 Carnegie Learning 300 Chapter Skills Practice

21 Lesson.3 Skills Practice page 5 Name Date 16. How man more games must Leon pla in order to score at least 100 points? f() # # # Leon must pla in 4 or more games to score at least 100 points. 17. How man more games must Leon pla in order to score fewer than 85 points? f() Leon must pla in or fewer games to score fewer than 85 points. 18. How man more games must Leon pla in order to score more than 00 points? f() , , , Leon must pla in 1 or more games to score more than 00 points. 01 Carnegie Learning Chapter Skills Practice 301

22 Lesson.3 Skills Practice page 6 Draw an oval on the graph to represent the solution to each question. Write the corresponding inequalit statement. 19. A hot air balloon at 4000 feet begins its descent. It descends at a rate of 00 feet per minute. The function f() represents the height of the balloon as it descends. How man minutes have passed if the balloon is below 3000 feet? Height (feet) More than 5 minutes have passed if the balloon is below 3000 feet Time (minutes) 0. A bathtub filled with 55 gallons of water is drained. The water drains at a rate of 5 gallons per minute. The function f() represents the volume of water in the tub as it drains. How man minutes have passed if the tub still has more than 0 gallons of water remaining in it? Volume (gallons) Time (minutes) Less than 7 minutes have passed if the tub has more than 0 gallons of water remaining in it., 7 01 Carnegie Learning 30 Chapter Skills Practice

23 Lesson.3 Skills Practice page 7 Name Date 1. Lea is walking to school at a rate of 50 feet per minute. Her school is 5000 feet from her home. The function f() 5 50 represents the distance Lea walks. How man minutes have passed if Lea still has more than 000 feet to walk? 4000 Less than 1 minutes have passed if Lea still has more than 000 feet to walk., 1 Distance (feet) Time (minutes). Franco is riding his bike to school at a rate of 600 feet per minute. His school is 9000 feet from his home. The function f() represents the distance Franco rides. How man minutes have passed if Franco has less than 3000 feet left to ride? 8000 More than 10 minutes have passed if Franco has less than 3000 feet to ride Carnegie Learning Distance (feet) Time (minutes) Chapter Skills Practice 303

24 Lesson.3 Skills Practice page 8 3. A submarine is diving from the surface of the water at a rate of 0 feet per minute. The function f() 5 0 represents the depth of the submarine as it dives. How man minutes have passed if the submarine is at least 160 feet below the surface? 00 At least 8 minutes have passed if the submarine is at least 160 feet below the surface. $ A scuba diver is diving from the surface of the water at a rate of 14 feet per minute. The function f() 5 14 represents the depth of the diver as he dives. How man minutes have passed if the diver is less than 4 feet below the surface? 60 Less than 3 minutes have passed if the diver is less than 4 feet below the surface., Carnegie Learning 304 Chapter Skills Practice

25 Lesson.4 Skills Practice Name Date We re Shipping Out! Solving and Graphing Compound Inequalities Vocabular Match each definition to its corresponding term. 1. compound inequalit b.. solution of a compound inequalit c. 3. conjunction a. 4. disjunction d. a. a solution of a compound inequalit in the form a,, b, where a and b are an real numbers b. an inequalit that is formed b the union, or, or the intersection, and, of two simple inequalities c. the part or parts of the solutions that satisf both of the inequalities d. a solution of a compound inequalit in the form, a or. b, where a and b are an real numbers Problem Set Write each compound inequalit in compact form. 1. All numbers less than or equal to and greater than 4 4. All numbers less than 55 and greater than Carnegie Learning 3. All numbers greater than or equal to 0 and less than or equal to All numbers greater than 10 and less than All numbers less than or equal to 87 and greater than or equal to All numbers greater than 1 and less than or equal to Chapter Skills Practice 305

26 Lesson.4 Skills Practice page Write an inequalit for each graph Graph each inequalit ,, Carnegie Learning Chapter Skills Practice

27 Lesson.4 Skills Practice page 3 Name Date Write a compound inequalit for each situation. 19. The flowers in the garden are 6 inches or taller or shorter than 3 inches. 6 or 3 0. People with a driver s license are at least 16 ears old and no older than 85 ears old Kle s car gets more than 31 miles per gallon on the highwa or 6 miles or less per gallon in the cit. 31 or 6. The number of houses that will be built in the new neighborhood must be at least 14 and no more than Carnegie Learning 3. At the High and Low Store, the sell high-end items that sell for over $1000 and low-end items that sell for less than $ or The heights of the twent tallest buildings in New York Cit range from 9 meters to 381 meters Chapter Skills Practice 307

28 Lesson.4 Skills Practice page 4 Represent the solution to each part of the compound inequalit on the number line. Then write the final solution that is represented b each graph. 5. and or or or and No solution 9. 1 or or 0 01 Carnegie Learning 308 Chapter Skills Practice

29 Lesson.4 Skills Practice page 5 Name Date and or All real numbers Solve each compound inequalit. Then graph and describe the solution. 01 Carnegie Learning Solution: Chapter Skills Practice 309

30 Lesson.4 Skills Practice page Solution: or or Solution: 9 or or or Solution: 01 Carnegie Learning 310 Chapter Skills Practice

31 Lesson.4 Skills Practice page 7 Name Date (8) ( 7 8 ) 8 7 (4) Solution: or or Solution: All real numbers 01 Carnegie Learning Chapter Skills Practice 311

32 01 Carnegie Learning 31 Chapter Skills Practice

33 Lesson.5 Skills Practice Name Date Pla Ball! Absolute Value Equations and Inequalities Vocabular Define each term in our own words. 1. opposites Opposites are two numbers that are equal distance, but are in different directions, from zero on the number line.. absolute value The absolute value of a number is its distance from zero on the number line. Give an eample of each term. 3. linear absolute value equation Answers will var linear absolute value inequalit Answers will var Match each equivalent compound inequalit to its corresponding absolute value inequalit. 01 Carnegie Learning 5. a 1 b, c a. 6. a 1 b # c c. 7. a 1 b. c b. 8. a 1 b $ c d. Problem Set a. c, a 1 b, c b. a 1 b, c or a 1 b. c c. c # a 1 b # c d. a 1 b # c or a 1 b $ c Evaluate each absolute value Chapter Skills Practice 313

34 Lesson.5 Skills Practice page Determine the number of solutions for each equation. Then calculate the solution There is onl one solution. There are no solutions There are two solutions. There are no solutions. 5 4 or There is onl one solution. There are two solutions or 5 15 Solve each linear absolute value equation ( 1 9) 5 ( 1 9) ( 1 4) 5 10 ( 1 4) ( 1) 5 5 ( 1) ( 6) 5 18 ( 6) Carnegie Learning 314 Chapter Skills Practice

35 Lesson.5 Skills Practice page 3 Name Date There are no solutions (5 1 1) 5 14 (5 1 1) Solve each linear absolute value equation () Carnegie Learning ( 1 3) 5 47 ( 1 3) ( 6) 5 4 ( 6) Chapter Skills Practice 315

36 Lesson.5 Skills Practice page ( 1 8) 5 1 ( 1 8) () () Solve each linear absolute value inequalit. Graph the solution on the number line , ( 1 5), ( 1 5), 1 5 5, , Carnegie Learning Chapter Skills Practice

37 Lesson.5 Skills Practice page 5 Name Date 6. 3 # 6 ( 3) # 6 ( 3) # # $ 6 # $ $ , 14 1, 14 1, 14 1, 7 ( 1), 7 ( 1), , , Carnegie Learning $ $ $ $ 3 ( 1 4) $ 3 ( 1 4) $ # $ # 3 4 $ 1 # Chapter Skills Practice 317

38 Lesson.5 Skills Practice page # # # # 18 1 # 18 1 # 9 ( 1) # 9 ( 1) # 9 1 $ # $ # 10 $ $ $ $ $ $ $ 6 ( 1 ) $ 6 ( 1 ) $ 6 1 # 6 1 $ 6 1 # 6 $ 4 # Carnegie Learning 318 Chapter Skills Practice

39 Lesson.5 Skills Practice page 7 Name Date 01 Carnegie Learning Graph the function that represents each problem situation. Draw an oval on the graph to represent the answer. 31. A jewelr compan is making 16-inch bead necklaces. The specifications allow for a difference of 0.5 inch. The function f() 5 16 represents the difference between the necklaces manufactured and the specifications. Graph the function. What necklace lengths meet the specifications? The necklaces can be between 15.5 and 16.5 inches long to meet the specifications. 3. Julian is cutting lengths of rope for a class project. Each rope length should be 10 inches long. The specifications allow for a difference of 1 inch. The function f() 5 10 represents the difference between the rope lengths cut and the specifications. Graph the function. What rope lengths meet the specifications? The rope lengths can be between 9 and 11 inches long to meet the specifications. 33. A snack compan is filling bags with pita chips sold b weight. Each bag should contain 8 ounces of chips. The specifications allow for a difference of 0.5 ounce. The function f() 5 8 represents the difference between the weight of a bag of chips and the specifications. Graph the function. What weights meet the specifications? Each bag of chips can weigh between 7.75 ounces and 8.5 ounces. Difference in Length (inches) Difference in Length (inches) Difference in Weight (ounces) Length of Necklace (inches) Rope Lengths (inches) Weight (ounces) Chapter Skills Practice 319

40 Lesson.5 Skills Practice page A cereal compan is filling boes with cereal sold b weight. Each bo should contain 3 ounces of cereal. The specifications allow for a difference of 0.5 ounce. The function f() 5 3 represents the difference between the weight of a bo of cereal and the specifications. Graph the function. What weights do not meet the specifications? A bo of cereal that weighs less than 31.5 ounces or more than 3.5 ounces does not meet the specifications. 35. Guests at the school harvest festival are asked to guess how man peanuts are in a jar. The jar contains 60 peanuts. All guests within 10 peanuts of the correct answer win a prize. The function f() 5 60 represents the difference between a guess and the actual number of peanuts in the jar. Graph the function. What possible guesses will not win a prize? A guess that is more than 70 or less than 50 will not win a prize. 36. The rules of an art contest state that sculptures submitted should be 3 feet high but allow for a difference of 6 inches. The function f() 5 3 represents the difference between a sculpture that is submitted and the specifications. Graph the function. What heights do not meet the specifications? A sculpture that is shorter than.5 feet or taller than 3.5 feet does not meet the specifications. Difference in Weight (ounces) Difference between Guess and Actual Number of Peanuts Difference in Height (feet) Weight (ounces) Number of Peanuts Guessed Height of Sculpture (feet) 01 Carnegie Learning 30 Chapter Skills Practice

41 Lesson.6 Skills Practice Name Date Choose Wisel! Understanding Non-Linear Graphs and Inequalities Problem Set Choose the function that represents each problem situation. 1. Tona is walking to school at a rate of 3 miles per hour. A f() 5 3 B f() 5 3 C f() 5 3 B f() 5 3. Guests at a craft fair are asked to guess how man beads are in a jar. The jar contains 0 beads. All guests within 10 beads of the correct answer win a prize. A f() 5 0 B f() 5 0 C f() 5 0 A f() Mario bus a car for $5,000. Each ear the car loses 1 of its value. 6 A f() 5 5, B f() ,000 C f() 5 5,000 ( 5 6 ) C f() 5 5,000 ( 5 6 ) 4. A bathtub filled with 50 gallons of water is drained. The water drains at a rate of 5 gallons per minute. A f() B f() C f() A f() Carnegie Learning 5. Rodell throws a football straight up with a speed of 5 feet per second. The acceleration of the ball due to gravit is 3 feet per second. A f() B f() C f() B f() A pasta compan is filling boes with pasta sold b weight. Each bo should contain 16 ounces of pasta. The specifications allow for a difference of 0.5 ounce. A f() B f() C f() 5 16 C f() 5 16 Chapter Skills Practice 31

42 Lesson.6 Skills Practice page Graph the function that represents each problem situation. Use the graph to answer the question. 7. A fish tank filled with 0 gallons of water is drained. The water drains at a rate of 4 gallons per minute. The function f() represents the volume of water in the fish tank as it drains. Graph the function. How man minutes does it take for half of the water to drain from the tank? Volume of Water (gallons) Time (minutes) After.5 minutes, half of the water in the tank (10 gallons) will be drained. 8. A pasta compan is filling boes with pasta sold b weight. Each bo should contain 3 ounces of pasta. The specifications allow for a difference of 1.5 ounces. The function f() 5 3 represents the difference between the weight of a bo of pasta and the specifications. Graph the function. What weights meet the specifications? Difference in Weight (ounces) Weight (ounces) Weights between 30.5 and 33.5 ounces meet the specifications. 01 Carnegie Learning 3 Chapter Skills Practice

43 Lesson.6 Skills Practice page 3 Name Date 9. Ronna bus a car for $0,000. Each ear the car loses 1 4 of its value. The function f() 5 0,000 ( 3 4 ) represents the value of the car over time. Graph the function. Ronna wants to eventuall sell the car and make at least $10,000 in the sale. Estimate the number of ears Ronna can own the car before she must resell and still make at least $10,000. Value of Car (dollars) 18,000 16,000 14,000 1,000 10, Time (ears) Ronna can own the car for almost.5 ears before reselling and will still make at least $10, Serena is driving to her aunt s house at a rate of 55 miles per hour. The function f() 5 55 represents the distance Serena travels over time. Graph the function. Estimate how long it will take Serena to get to her aunt s house which is 19 miles awa. 01 Carnegie Learning Distance (miles) Time (hours) It will take Serena about 3.5 hours to reach her aunt s house. Chapter Skills Practice 33

44 Lesson.6 Skills Practice page Hector throws a softball straight up with a speed of 50 feet per second. The acceleration of the ball due to gravit is 3 feet per second. The function f() represents the height of the softball as it travels up in the air and back to the ground. Graph the function. Estimate the length of time the softball is in the air. Height (feet) Time (seconds) The softball is in the air for about 1.5 seconds. 1. Guests at a craft fair are asked to guess how man beads are in a jar. The jar contains 180 beads. All guests within 0 beads of the correct answer win a prize. The function f() represents the difference between a guess and the actual number of beads in the jar. Graph the function. What possible guesses will win a prize? Difference between Guess and Actual Number of Beads Number of Beads Guessed 01 Carnegie Learning Guesses that are between 160 beads and 00 beads will win a prize. 34 Chapter Skills Practice