In Problems 1–6, find the real solutions of each equation. 1. x3 8 10 − = 2. x x 3 0 2 − = 3. x x8 9 0 2 − − = 4. x x 6 5 1 0 2 − + = 5. x2 3 4 + = 6. x2 3 2 + = In Problems 7–9, solve each inequality. Graph the solution set. 7. x 2 3 6 − > 8. x2 5 3 − < 9. x4 1 7 + ≥ 10. (a) Find the distance from P 2, 3 1 ( ) = − − to P 3, 5. 2 ( ) = − (b) What is the midpoint of the line segment from P1 to P ?2 (c) What is the slope of the line containing the points P1 and P ?2 In Problems 11–14, graph each equation. 11. x y 3 2 12 − = 12. x y2 = 13. x y 3 16 2 2 ( ) + − = 14. y x = 15. For the equation x y 3 4 12, 2 − = find the intercepts and check for symmetry. 16. Find the slope–intercept form of the equation of the line containing the points 2, 4 ( ) − and 6,8 . ( ) In Problems 17–19, graph each function. 17. f x x 2 3 2 ( ) ( ) = + − 18. f x x 1 ( ) = 19. f x x x x x 2 if 2 if 2 ( ) = − ≤ > ⎧ ⎨ ⎪⎪ ⎩ ⎪⎪ Cumulative Review Chapter Project Choosing a Data Plan Collect information from your family, friends, or consumer agencies such as Consumer Reports. Then decide on a service provider, choosing the company that you feel offers the best service. Once you have selected a service provider, research the various types of individual plans offered by the company by visiting the provider’s website. Many cellular providers offer family plans that include unlimited talk, text, and data. However, once a data cap has been reached, service may be slowed, which prevents media from being streamed. So, many customers still purchase data-only plans for devices such as tablets or laptops. The monthly cost is primarily determined by the amount of data used and the number of data-only devices. 1. Suppose you expect to use 10 gigabytes of data for a single tablet. What would be the monthly cost of each plan you are considering? 2. Suppose you expect to use 30 gigabytes of data and want a personal hotspot, but you still have only a single tablet. What would be the monthly cost of each plan you are considering? 3. Suppose you expect to use 20 gigabytes of data with three tablets sharing the data. What would be the monthly cost of each plan you are considering? 4. Suppose you expect to use 20 gigabytes of data with a single tablet and a personal hotspot.What would be the monthly cost of each plan you are considering? 5. Build a model that describes the monthly cost C, in dollars, as a function of the number g of data gigabytes used, assuming a single tablet and a personal hotspot for each plan you are considering. 6. Graph each function from Problem 5. 7. Based on your particular usage, which plan is best for you? 8. Now, develop an Excel spreadsheet to analyze the various plans you are considering. Suppose you want a plan that offers 50 gigabytes of shared data and costs $60 per month. Additional gigabytes of data cost $15 per gigabyte, extra tablets can be added to the plan for $10 each per month, and each hotspot or laptop costs $20 per month. Because these data plans have a cost structure based on piecewise-defined functions, we need an “if/then” statement within Excel to analyze the cost of the plan. Use the accompanying Excel spreadsheet as a guide in developing your spreadsheet. Enter into your spreadsheet a variety of possible amounts of data and various numbers of additional tablets, laptops, and hotspots. Credit: Oleksiy Mark/Shutterstock Internet-based Project 136 CHAPTER 2 Functions and Their Graphs
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