By Amodei L., Dedieu J.-P.

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20, which is the graph of y 2x Ϫ 1. 20 4 x 20 Chapter 1 Functions and Graphs EXAMPLE 2 » Draw a Graph by Plotting Points Graph: Ϫx 2 ϩ y 1 Solution Solve the equation for y. Ϫx 2 ϩ y 1 y x2 ϩ 1 y (− 2, 5) (2, 5) 4 (−1, 2) • Add x 2 to each side. Select values of x and use the equation to calculate y. Choose enough values of x so that an accurate graph can be drawn. Plot the points and draw a smooth curve through them. 21. 21 x y ؍x2 ؉ 1 y (x, y) Ϫ2 2 ͑Ϫ2͒ ϩ 1 5 ͑Ϫ2, 5͒ Ϫ1 ͑Ϫ1͒ ϩ 1 2 ͑Ϫ1, 2͒ 0 ͑0͒ ϩ 1 1 ͑0, 1͒ 1 ͑1͒2 ϩ 1 2 ͑1, 2͒ 2 ͑2͒ ϩ 1 5 ͑2, 5͒ 2 2 2 » Try Exercise 26, page 28 Integrating Technology Some graphing calculators, such as the TI-83/TI-83 Plus/TI-84 Plus, have a TABLE feature that allows you to create a table similar to the one shown in Example 2.

As the values of x increase, do the values of y increase or decrease? 30 defines a correspondence between the length of a pendulum and the time it takes the pendulum to complete one oscillation. For each nonnegative pendulum length, the graph yields only one time. 2 seconds, where the time is measured to the nearest tenth of a second. 2͒. 1 In many situations in science, business, and mathematics, a correspondence exists between two sets. The correspondence is often defined by a table, an equation, or a graph, each of which can be viewed from a mathematical perspective as a set of ordered pairs.

3͑x ϩ 2͒ Յ 5x ϩ 7 56. Ϫ4͑x Ϫ 5͒ Ն 2x ϩ 15 57. Ϫ4͑3x Ϫ 5͒ Ͼ 2͑x Ϫ 4͒ 58. 3͑x ϩ 7͒ Յ 5͑2x Ϫ 8͒ 17. 12͑4000 Ϫ x͒ 432 18. 50 In Exercises 19 to 26, solve each equation for the indicated variable. 19. x ϩ 2y 8; y 20. 3x Ϫ 5y 15; y 21. 2x ϩ 5y 10; x 22. 5x Ϫ 4y 10; x 23. ay Ϫ by c; y 24. ax ϩ by c; y 25. x y ;y 1Ϫy 26. x 2y Ϫ 3 ;y yϪ1 In Exercises 27 to 40, solve by using the quadratic formula. 27. x 2 Ϫ 2x Ϫ 15 0 28. x 2 Ϫ 5x Ϫ 24 0 29. x 2 ϩ x Ϫ 1 0 30. x 2 ϩ x Ϫ 2 0 31. 2x 2 ϩ 4x ϩ 1 0 32.