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C H A P T E R 1

C H A P T E R 1. Functions, Graphs, and Limits. Figure 1.1 Interpretations of the function f ( x ). 1-1-1. Figure 1.2 The composition f ( g ( x )) as an assembly line. 1-1-2. Figure 1.3 (a) A production function. (b) Bounded population growth. 1-2-3.

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C H A P T E R 1

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  1. C H A P T E R 1 Functions, Graphs, and Limits

  2. Figure 1.1 Interpretations of the function f(x). 1-1-1

  3. Figure 1.2 The composition f(g(x)) as an assembly line. 1-1-2

  4. Figure 1.3 (a) A production function. (b) Bounded population growth. 1-2-3

  5. Figure 1.4 (a) The graph of y = x2. (b) Other graphs through the points in Example 2.1. 1-2-4

  6. Figure 1.5 The graph of f(x) = 1-2-5

  7. Figure 1.6 The graph of f(x) = –x2 + x + 2. 1-2-6

  8. Figure 1.7 The graph of the functiony = x3 – x2 – 6x. 1-2-7

  9. Figure 1.8The graph of the parabola y = Ax2 + Bx + C. (a) If A > 0, the parabola opens up. (b) If A < 0, the parabola opens down. 1-2-8

  10. Figure 1.9 A revenue function. 1-2-9

  11. Figure 1.10 The graphs of y = f(x) and y = g(x) intersect at P and Q. 1-2-10

  12. Figure 1.11 The intersection of the graphs off(x) = 3x + 2 and g(x) = x2. 1-2-11

  13. Figure 1.12 Three polynomials of degree 3. 1-2-12

  14. Figure 1.13 Graphs of three rational functions. 1-2-13

  15. Figure 1.14 The vertical line test. 1-2-14

  16. Figure 1.15 The cost function C(x) = 50x + 200. 1-3-15

  17. Figure 1.16 1-3-16

  18. Figure 1.17 The line joining (–2, 5) and (3, –1). 1-3-17

  19. Figure 1.18 The direction and steepness of a line. 1-3-18

  20. Figure 1.19 Horizontal and vertical lines. 1-3-19

  21. Figure 1.20 The slope and y intercept of the liney = mx + b. 1-3-20

  22. Figure 1.21 The line 3y + 2x = 6. 1-3-21

  23. Figure 1.22 The line 1-3-22

  24. Figure 1.23 The line y = –4x + 10. 1-3-23

  25. Figure 1.24 The rising price of bread: y = 2x + 136. 1-3-24

  26. Figure 1.25 Growth of federal civilian employment in the United States (1950–1989). 1-3-25

  27. Figure 1.26 1-3-26

  28. Figure 1.27 Lines parallel and perpendicularto a given line L. 1-3-27

  29. Figure 1.28 Rectangular picnic area. 1-4-28

  30. Figure 1.29 The length of fencing: 1-4-29

  31. Figure 1.30 Cylindrical can for Example 4.2. 1-4-30

  32. Figure 1.31 The cost function: 1-4-31

  33. Figure 1.32 The cost of water in Marin County. 1-4-32

  34. Figure 1.33 The rate of bounded population growth: R(p) = kp(b – p). 1-4-33

  35. Figure 1.34 The profit functionP(x) = (6,000 – 400x)(x – 2). 1-4-34

  36. Figure 1.35 Market equilibrium: the intersection of supply and demand. 1-4-35

  37. Figure 1.36 The supply and demand curvesfor Example 4.6. 1-4-36

  38. 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. Figure 1.38 Three functions for which 1-5-38

  40. Figure 1.39 Two functions for which does not exist. 1-5-39

  41. Figure 1.40 Limits of two linear functions. 1-5-40

  42. Figure 1.41 The graph of 1-5-41

  43. Figure 1.42 The graph of 1-5-42

  44. Figure 1.43 Just in time inventory. 1-5-43

  45. Figure 1.44 The graph of 1-5-44

  46. Figure 1.45 A continuous graph. 1-6-45

  47. Figure 1.46 Three functions with discontinuities of x = c. 1-6-46

  48. Figure 1.47 Functions for Example 6.3. 1-6-47

  49. Figure 1.48 The graph of 1-6-48

  50. Figure 1.49 The intermediate value property. 1-6-49

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