1. Chapter 1 Linear Functions Table of Contents 1.1 Solving Linear Equations 1.2 Using Data to Create Scatterplots 1.3 Fundamentals of Graphing and Slope 1.4 Intercepts and Graphing 1.5 Finding Equations of Lines 1.6 Finding Linear Models 1.7 Functions and Function Notation

2. You plan to purchase custom printed lunch coolers for your school staff. If you order 50 or more lunch coolers, there will be a $45 setup fee and each lunch cooler will cost $3. a.Write an equation for the total cost, C, in dollars for purchasing L lunch coolers. b.How much would 75 lunch coolers cost? 1.1-1 2 Back to Table of Contents

3. c.How many lunch coolers can you purchase with a budget of $400? 1.1-1 3 Back to Table of Contents

4. Golf Carts To Go sells refurbished golf carts in south Florida. The company has fixed costs of $26,000 per month for rent, salary and utilities. They can buy used carts and refurbish them for an average of $1,400 each. They sell the carts for an average price of $2500 each. Golf Carts To Go can only refurbish 55 carts a month. a.Write an equation for the monthly cost of refurbishing n carts. 1.1-2 4 Back to Table of Contents

5. Golf Carts To Go sells refurbished golf carts in south Florida. The company has fixed costs of $26,000 per month for rent, salary and utilities. They can buy used carts and refurbish them for an average of $1,400 each. They sell the carts for an average price of $2500 each. Golf Carts To Go can only refurbish 55 carts a month. b.Write an equation for the monthly revenue from selling golf carts. 1.1-2 5 Back to Table of Contents

6. Golf Carts To Go sells refurbished golf carts in south Florida. The company has fixed costs of $26,000 per month for rent, salary and utilities. They can buy used carts and refurbish them for an average of $1,400 each. They sell the carts for an average price of $2500 each. Golf Carts To Go can only refurbish 55 carts a month. c.Write an equation for the monthly profit the company makes if they refurbish and sell n carts. 1.1-2 6 Back to Table of Contents

7. d.What is the profit of refurbishing and selling 25 golf carts? 1.1-2 7 Back to Table of Contents

8. e.How many golf carts does the company have to refurbish and sell to earn $20,000 profit? 1.1-2 8 Back to Table of Contents

9. Golf Carts To Go can only refurbish 55 carts a month. f.How many golf carts does the company have to refurbish and sell to earn $40,000 profit? 1.1-2 9 Back to Table of Contents

10. Solve 1.1-3 10 Back to Table of Contents

11. Solve 1.1-3 11 Back to Table of Contents

12. Solvefor p. Solve for r. 1.1-4 12

13. Solve for x. 1.1-4 13 Back to Table of Contents

14. Create a scatterplot of the data given in the table. The percent of adults aged 20 years and over in the United States who are considered obese are given in the table. Source: CDC 2008 National Health Interview Survey. 1.2-1 YearPercent 200424.5 200525.4 200626.4 200726.7 200826.8 14 Back to Table of Contents

15. a.Using the scatterplot of the obesity data from before, draw an “eyeball best fit” line through the data. 1.2-2 15 Back to Table of Contents

16. 1.2-1 b. Using your eyeball best-fit line, make a prediction for the percentage of adults in the United States who were considered obese in 2010. 16 Back to Table of Contents

17. Use the graph to answer the following questions a.Estimate the vertical intercept. b.Estimate the horizontal intercept. 1.2-3 17 Back to Table of Contents

18. Use the graph to answer the following questions c. Estimate the input value that makes the output of this graph equal 3. d. Estimate the output value of this graph when the input value is. 1.2-3 18 Back to Table of Contents

19. Determine a reasonable domain and range for the graphical model found for the obesity data. 1.2-4 19 Back to Table of Contents

20. The percentage of students in twelfth grade who report smoking daily is given in the table. Source: www.monitoringthefuture.org a.Create a scatterplot for these data and draw an “eyeball best fit” line through the data.www.monitoringthefuture.org 1.2-5 YearPercent 200020.6 200119.0 200216.9 200315.8 200415.6 200513.6 200612.2 20 Back to Table of Contents

21. Answer: t = years since 2000. P = percent of twelfth grade students who report smoking daily. 1.2-5 21 Back to Table of Contents

22. b.Determine the vertical intercept for this model. Explain its meaning in this situation. c.Find a reasonable domain and range for this model. 1.2-5 22 Back to Table of Contents

23. d.According to your graphical model, what percentage of twelfth grade students reported smoking daily in 2007? 1.2-5 23 Back to Table of Contents

24. Graph the equations by creating a table of values and plotting the points. a.b. 1.3-1 24 Back to Table of Contents

25. An equation for the total cost, C, in dollars for purchasing L lunch coolers is. a.Create a table of points that satisfy this equation. 1.3-2 25 Back to Table of Contents

26. An equation for the total cost, C, in dollars for purchasing L lunch coolers is. b.Create a graph for the equation using your points. Label your graph with units. 1.3-2 26 Back to Table of Contents

27. An equation for the total cost, C, in dollars for purchasing L lunch coolers is. b.Create a graph for the equation using your points. Label your graph with units. 1.3-2 27 Back to Table of Contents

28. Use the graph to estimate the slope of the line and determine if the line is increasing or decreasing. 1.3-3 28 Back to Table of Contents

29. Find the slope of the line passing through the points given in the table. 1.3-4 xy 5 86 29 Back to Table of Contents

30. Determine if the points given in the table all lie on a line. a. 1.3-5 30 Back to Table of Contents xy 611 1016 1218.5 2231

31. Determine if the points given in the table all lie on a line. b. 1.3-5 xy 5.4 23.4 42.8 81 31 Back to Table of Contents

32. Find the slope and y-intercept of the following lines. a.b. 1.3-6 32 Back to Table of Contents

33. Find the slope and y-intercept of the following lines. c. 1.3-6 33 Back to Table of Contents

34. Find the slope of the model and explain its meaning in the given situation. a.Let be the total cost in dollars to produce p pizzas a day at a local pizzeria. 1.3-7 34 Back to Table of Contents

35. Find the slope of the model and explain its meaning in the given situation. b.Letbe the percentage of adults aged 18 years old and over in the United States that have been diagnosed with diabetes, t years since 2000. Source: CDC. 1.3-7 35 Back to Table of Contents

36. Sketch the graph of the following lines. Label the vertical intercept. a.b. 1.3-8 36 Back to Table of Contents

37. Rewrite the following equations in general form. a.b. 1.4-1 37 Back to Table of Contents

38. Find the vertical and horizontal intercepts, and explain their meaning in the given situation. Let be the percentage of adults aged 18 years old and over in the United States that have been diagnosed with diabetes, t years since 2000. Source: CDC. 1.4-2 38 Back to Table of Contents

39. Find the horizontal and vertical intercepts of 1.4-3 39 Back to Table of Contents

40. Find the intercepts and graph the line 1.4-4 40 Back to Table of Contents

41. Sketch the graph of the following lines a. 1.4-5 41 Back to Table of Contents

42. Sketch the graph of the following lines b. 1.4-5 42 Back to Table of Contents

43. Write the equation of the line that passes through the points (4,3) and (20,-17) 1.5-1 43 Back to Table of Contents

44. A business purchased a production machine in 2005 for $185,000. For tax purposes, the value of the machine in 2011 was $129,500. If the business is using straight line depreciation, write the equation of the line that gives the value of the machine based on the age of the machine in years. 1.5-2 44 Back to Table of Contents

45. According to www.childtrendsdatabank.org the number of newly diagnosed AIDS cases for adolescents 13-19 years old in the United States was 310 in 2000 and 458 in 2003. Assume that the number of cases is growing at a constant rate, and write an equation to represent this situation.www.childtrendsdatabank.org 1.5-3 45 Back to Table of Contents

46. Use the point slope formula to write the equation of the line that passes through the points and. 1.5-4 46 Back to Table of Contents

47. a.Write the equation of the line that passes through the points in the table. 1.5-5 xy 513 715.8 1527 1831.2 47 Back to Table of Contents

48. b.Write the equation of the line shown in the graph. 1.5-5 48 Back to Table of Contents

49. a.Write the equation of the line that goes through the point and is perpendicular to the line. 1.5-6 49 Back to Table of Contents

50. b.Write the equation of the line that goes through the point (8,11) and is parallel to the line. 1.5-6 50 Back to Table of Contents

51. Using the value of the production machine equation we found earlier, answer the following: a.What is the slope of the equation? What does it represent in regards to the value of the machine? b.What is the vertical intercept of the equation? What does it represent in this situation? 1.5-7 51 Back to Table of Contents

52. Using the value of the production machine equation we found earlier, answer the following: c.What is the horizontal intercept of the equation? What does it represent in this situation? 1.5-7 52 Back to Table of Contents

53. Using the AIDS equation found in classroom example 3, answer the following: a.What is the slope of the equation? What does it mean in this situation? b.What is the vertical intercept for the equation? What does it represent in this situation? 1.5-8 53 Back to Table of Contents

54. There were 44.1 million major home appliances shipped in the United States in 2007. In 2009 only 36.7 million were shipped. Source: Association of Home Appliance Manufacturers. a.Write an equation for the number of major home appliances shipped in the US t years since 2000. b.What is the slope of the equation found in part a? What does it represent? 1.5-9 54 Back to Table of Contents

55. There were 44.1 million major home appliances shipped in the United States in 2007. In 2009 only 36.7 million were shipped. Source: Association of Home Appliance Manufacturers. c.What is the vertical intercept for the equation you found in part a? What does it represent? 1.5-9 55 Back to Table of Contents

56. Create a scatter plot on your graphing calculator for the population data for North Carolina given in the table. Source: Population Division, U.S. Census Bureau 1.6-1 Year Population (millions) 20038.41 20048.52 20058.66 20068.85 20079.04 20089.22 56 Back to Table of Contents

57. Find an equation for a model of the population of North Carolina data given earlier. 1.6-2 57 Back to Table of Contents

58. The total revenue for GE is given in the table. Source: GE 2008 annual report a.Find an equation for a model of these data. 1.6-3 Year Revenue (billions $) 2004124 2005136 2006152 2007172 2008183 58 Back to Table of Contents

59. The total revenue for GE is given in the table. b.Using your model estimate GE’s revenue in 2010. c.What is the slope of your model? What does it mean in regards to GE’s revenue? d.Determine a reasonable domain and range for the model. 1.6-3 YearRevenue (billions $) 2004124 2005136 2006152 2007172 2008183 59 Back to Table of Contents

60. Determine whether the following descriptions of relations are functions or not. a.The set b. c.Weekly salaries during the mth month of the year. 1.7-1 Day of weekMondayWednesdaySaturdayMonday Temperature degrees Fahrenheit 90889193 60 Back to Table of Contents

61. a.Is the equation a function or not? b.Is the equation a function or not? 1.7-2 61 Back to Table of Contents

62. c.Does the graph represent a function? 1.7-2 62 Back to Table of Contents

63. = The height of a toy rocket in feet t second after launch. Interpret the mathematical statement. 1.7-3 63 Back to Table of Contents

64. The population of Wisconsin, in millions, is given in the table. Source: www.census.gov Let P(t) be the population of Wisconsin, in millions, t years since 2000. a.Find an equation for a model of these data. Write your model in function notation. b.Determine a reasonable domain and range for your model.www.census.gov 1.7-4 Year Population (in millions) 20035.47 20045.51 20055.54 20065.57 20075.60 20085.63 64 Back to Table of Contents

65. The population of Wisconsin, in millions, is given in the table. Source: www.census.gov c.Find P(14) and interpret its meaning in regard to the population of Wisconsin. d.Find when P(t) = 5.75 and interpret its meaning in regard to the population of Wisconsin.www.census.gov 1.7-4 Year Population (in millions) 20035.47 20045.51 20055.54 20065.57 20075.60 20085.63 65 Back to Table of Contents

66. Let Find the following. a. 1.7-5 66 Back to Table of Contents

67. Let Find the following. b. 1.7-5 67 Back to Table of Contents

68. Let Find the following. c.x such that 1.7-5 68 Back to Table of Contents

69. Use the graph to estimate the following. a. b. x such that 1.7-6 69 Back to Table of Contents

70. Determine the domain and range of the following functions a. b. 1.7-7 70 Back to Table of Contents