1. Copyright © 2000 by the McGraw-Hill Companies, Inc. C H A P T E R 1 Functions, Graphs, and Limits

2. Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.1 Interpretations of the function f(x). 1-1-1

3. Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.2 The composition f(g(x)) as an assembly line. 1-1-2

4. Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.3 (a) A production function. (b) Bounded population growth. 1-2-3

5. Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.4 (a) The graph of y = x 2. (b) Other graphs through the points in Example 2.1. 1-2-4

6. Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.5 The graph of f(x) = 1-2-5

7. Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.6 The graph of f(x) = –x 2 + x + 2. 1-2-6

8. Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.7 The graph of the function y = x 3 – x 2 – 6x. 1-2-7

9. Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.8 The graph of the parabola y = Ax 2 + Bx + C. (a) If A > 0, the parabola opens up. (b) If A < 0, the parabola opens down. 1-2-8

10. Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.9 A revenue function. 1-2-9

11. Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.10 The graphs of y = f(x) and y = g(x) intersect at P and Q. 1-2-10

12. Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.11 The intersection of the graphs of f(x) = 3x + 2 and g(x) = x 2. 1-2-11

13. Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.12 Three polynomials of degree 3. 1-2-12

14. Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.13 Graphs of three rational functions. 1-2-13

15. Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.14 The vertical line test. 1-2-14

16. Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.15 The cost function C(x) = 50x + 200. 1-3-15

17. Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.16 1-3-16

18. Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.17 The line joining (–2, 5) and (3, –1). 1-3-17

19. Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.18 The direction and steepness of a line. 1-3-18

20. Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.19 Horizontal and vertical lines. 1-3-19

21. Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.20 The slope and y intercept of the line y = mx + b. 1-3-20

22. Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.21 The line 3y + 2x = 6. 1-3-21

23. Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.22 The line 1-3-22

24. Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.23 The line y = –4x + 10. 1-3-23

25. Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.24 The rising price of bread: y = 2x + 136. 1-3-24

26. Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.25 Growth of federal civilian employment in the United States (1950–1989). 1-3-25

27. Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.26 1-3-26

28. Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.27 Lines parallel and perpendicular to a given line L. 1-3-27

29. Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.28 Rectangular picnic area. 1-4-28

30. Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.29 The length of fencing: 1-4-29

31. Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.30 Cylindrical can for Example 4.2. 1-4-30

32. Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.31 The cost function: 1-4-31 rC(r) 0.5608 1.0320 1.5243 2.0226 2.5238 3.0270

33. Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.32 The cost of water in Marin County. 1-4-32 xC(x) 00 1214.64 24134.64 30434.64

34. Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.33 The rate of bounded population growth: R(p) = kp(b – p). 1-4-33

35. Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.34 The profit function P(x) = (6,000 – 400x)(x – 2). 1-4-34

36. Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.35 Market equilibrium: the intersection of supply and demand. 1-4-35

37. Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.36 The supply and demand curves for Example 4.6. 1-4-36

38. Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.37 Geometric interpretation of the limit. (a) If the height of the graph of f approaches L as x approaches c. (b) Geometric interpretation of the limit statement 1-5-37

39. Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.38 Three functions for which 1-5-38

40. Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.39 Two functions for which does not exist. 1-5-39

41. Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.40 Limits of two linear functions. 1-5-40

42. Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.41 The graph of 1-5-41

43. Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.42 The graph of 1-5-42

44. Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.43 Just in time inventory. 1-5-43

45. Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.44 The graph of 1-5-44

46. Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.45 A continuous graph. 1-6-45

47. Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.46 Three functions with discontinuities of x = c. 1-6-46

48. Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.47 Functions for Example 6.3. 1-6-47

49. Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.48 The graph of 1-6-48

50. Copyright © 2000 by the McGraw-Hill Companies, Inc. Figure 1.49 The intermediate value property. 1-6-49

51. Copyright © 2000 by the McGraw-Hill Companies, Inc. 1-6-50 Figure 1.50 The graph of