1. Lial/Hungerford/Holcomb/Mullin: Mathematics with Applications 11e Finite Mathematics with Applications 11e
Copyright ©2015 Pearson Education, Inc. All right reserved.

2. Copyright ©2015 Pearson Education, Inc. All right reserved.
Chapter 3
Functions and Graphs
Copyright ©2015 Pearson Education, Inc. All right reserved.

3. Copyright ©2015 Pearson Education, Inc. All right reserved.
Section 3.1
Functions
Copyright ©2015 Pearson Education, Inc. All right reserved.

4. Copyright ©2015 Pearson Education, Inc. All right reserved.

5. Copyright ©2015 Pearson Education, Inc. All right reserved.

6. Copyright ©2015 Pearson Education, Inc. All right reserved.

7. Copyright ©2015 Pearson Education, Inc. All right reserved.

8. Copyright ©2015 Pearson Education, Inc. All right reserved.
Example:
Each of the given equations defines y as a function of x. Find the domain of each function.
(a)
Solution:
Any number can be raised to the fourth power, so the domain is the set of all real numbers, which is sometimes written as
(b)
Solution:
For y to be a real number, must be nonnegative. This happens only when —that is, when So the domain is the interval
(c)
Solution:
Because the denominator cannot be 0, and the domain consists of all numbers in the intervals,
Copyright ©2015 Pearson Education, Inc. All right reserved.

9. Copyright ©2015 Pearson Education, Inc. All right reserved.

10. Copyright ©2015 Pearson Education, Inc. All right reserved.
Section 3.2
Graphs and Functions
Copyright ©2015 Pearson Education, Inc. All right reserved.

11. Copyright ©2015 Pearson Education, Inc. All right reserved.

12. Copyright ©2015 Pearson Education, Inc. All right reserved.

13. Copyright ©2015 Pearson Education, Inc. All right reserved.

14. Graph the absolute-value function, whose rule is
Example:
Graph the absolute-value function, whose rule is
Solution:
The absolute value function can be defined as the piecewise function
So the right half of the graph (that is, where ) will consist of a portion of the line It can be graphed by plotting two points, say
The left half of the graph (where ) will consist of a portion of the line which can be graphed by plotting
Copyright ©2015 Pearson Education, Inc. All right reserved.

15. Copyright ©2015 Pearson Education, Inc. All right reserved.

16. Copyright ©2015 Pearson Education, Inc. All right reserved.

17. Copyright ©2015 Pearson Education, Inc. All right reserved.

18. Copyright ©2015 Pearson Education, Inc. All right reserved.

19. Copyright ©2015 Pearson Education, Inc. All right reserved.

20. Copyright ©2015 Pearson Education, Inc. All right reserved.

21. Copyright ©2015 Pearson Education, Inc. All right reserved.

22. Copyright ©2015 Pearson Education, Inc. All right reserved.

23. Copyright ©2015 Pearson Education, Inc. All right reserved.

24. Copyright ©2015 Pearson Education, Inc. All right reserved.

25. Copyright ©2015 Pearson Education, Inc. All right reserved.

26. Copyright ©2015 Pearson Education, Inc. All right reserved.

27. Applications of Linear Functions
Section 3.3
Applications of Linear Functions
Copyright ©2015 Pearson Education, Inc. All right reserved.

28. Copyright ©2015 Pearson Education, Inc. All right reserved.
Example:
An anticlot drug can be made for $10 per unit. The total cost to produce 100 units is $1500.
(a) Assuming that the cost function is linear, find its rule.
Solution:
Since the cost function is linear, its rule is of the form
We are given that m (the cost per item) is 10, so the rule is
To find b, use the fact that it costs $1500 to produce 100 units which means that
So the rule is
(b) What are the fixed costs?
Solution:
The fixed costs are
Copyright ©2015 Pearson Education, Inc. All right reserved.

29. Copyright ©2015 Pearson Education, Inc. All right reserved.

30. Copyright ©2015 Pearson Education, Inc. All right reserved.

31. Copyright ©2015 Pearson Education, Inc. All right reserved.

32. Copyright ©2015 Pearson Education, Inc. All right reserved.

33. Copyright ©2015 Pearson Education, Inc. All right reserved.

34. Copyright ©2015 Pearson Education, Inc. All right reserved.

35. Copyright ©2015 Pearson Education, Inc. All right reserved.

36. Copyright ©2015 Pearson Education, Inc. All right reserved.
Section 3.4
Quadratic Functions
Copyright ©2015 Pearson Education, Inc. All right reserved.

37. Graph each of these quadratic functions:
Example:
Graph each of these quadratic functions:
Solution:
In each case, choose several numbers (negative, positive, and 0) for x, find the values of the function at these numbers, and plot the corresponding points. Then connect the points with a smooth curve to obtain the graphs.
Copyright ©2015 Pearson Education, Inc. All right reserved.

38. Copyright ©2015 Pearson Education, Inc. All right reserved.

39. Copyright ©2015 Pearson Education, Inc. All right reserved.

40. Copyright ©2015 Pearson Education, Inc. All right reserved.

41. Copyright ©2015 Pearson Education, Inc. All right reserved.

42. Copyright ©2015 Pearson Education, Inc. All right reserved.

43. Copyright ©2015 Pearson Education, Inc. All right reserved.

44. Copyright ©2015 Pearson Education, Inc. All right reserved.

45. Copyright ©2015 Pearson Education, Inc. All right reserved.

46. Copyright ©2015 Pearson Education, Inc. All right reserved.

47. Copyright ©2015 Pearson Education, Inc. All right reserved.

48. Copyright ©2015 Pearson Education, Inc. All right reserved.

49. Copyright ©2015 Pearson Education, Inc. All right reserved.

50. Copyright ©2015 Pearson Education, Inc. All right reserved.

51. Copyright ©2015 Pearson Education, Inc. All right reserved.

52. Copyright ©2015 Pearson Education, Inc. All right reserved.
Section 3.5
Polynomial Functions
Copyright ©2015 Pearson Education, Inc. All right reserved.

53. Copyright ©2015 Pearson Education, Inc. All right reserved.
Example:
Graph
Solution:
First, find several ordered pairs belonging to the graph. Be sure to choose some negative x-values, and some positive x-values in order to get representative ordered pairs. Find as many ordered pairs as you need in order to see the shape of the graph and draw a smooth curve through them to obtain the graph below.
Copyright ©2015 Pearson Education, Inc. All right reserved.

54. Copyright ©2015 Pearson Education, Inc. All right reserved.

55. Copyright ©2015 Pearson Education, Inc. All right reserved.

56. Copyright ©2015 Pearson Education, Inc. All right reserved.

57. Copyright ©2015 Pearson Education, Inc. All right reserved.

58. Copyright ©2015 Pearson Education, Inc. All right reserved.

59. Copyright ©2015 Pearson Education, Inc. All right reserved.

60. Copyright ©2015 Pearson Education, Inc. All right reserved.

61. Copyright ©2015 Pearson Education, Inc. All right reserved.

62. Copyright ©2015 Pearson Education, Inc. All right reserved.

63. Copyright ©2015 Pearson Education, Inc. All right reserved.

64. Copyright ©2015 Pearson Education, Inc. All right reserved.

65. Copyright ©2015 Pearson Education, Inc. All right reserved.

66. Copyright ©2015 Pearson Education, Inc. All right reserved.

67. Copyright ©2015 Pearson Education, Inc. All right reserved.

68. Copyright ©2015 Pearson Education, Inc. All right reserved.

69. Copyright ©2015 Pearson Education, Inc. All right reserved.
Section 3.6
Rational Functions
Copyright ©2015 Pearson Education, Inc. All right reserved.

70. Copyright ©2015 Pearson Education, Inc. All right reserved.

71. Copyright ©2015 Pearson Education, Inc. All right reserved.

72. Copyright ©2015 Pearson Education, Inc. All right reserved.

73. Copyright ©2015 Pearson Education, Inc. All right reserved.

74. Copyright ©2015 Pearson Education, Inc. All right reserved.

75. Copyright ©2015 Pearson Education, Inc. All right reserved.

76. Copyright ©2015 Pearson Education, Inc. All right reserved.
Example:
Graph
Solution:
Find the vertical asymptotes by setting the denominator equal to 0 and solving for x:
Factor.
Set each term equal to 0.
Solve for x.
Since neither of these numbers makes the numerator 0, the lines
are vertical asymptotes of the graph.
Copyright ©2015 Pearson Education, Inc. All right reserved.

77. Copyright ©2015 Pearson Education, Inc. All right reserved.
Example:
Graph
Solution:
The horizontal asymptote can be determined by dividing both the numerator and denominator of by (the highest power of x that appears in either one).
When is very large, the fraction is very close to 0, so the denominator is very close to 1 and is very close to 2. Hence, the line is the horizontal asymptote of the graph.
Copyright ©2015 Pearson Education, Inc. All right reserved.

78. Copyright ©2015 Pearson Education, Inc. All right reserved.
Example:
Graph
Solution:
Using this information and plotting several points in each of the three regions defined by the vertical asymptotes, we obtain the desired graph.
Copyright ©2015 Pearson Education, Inc. All right reserved.

79. Copyright ©2015 Pearson Education, Inc. All right reserved.

80. Copyright ©2015 Pearson Education, Inc. All right reserved.

81. Copyright ©2015 Pearson Education, Inc. All right reserved.

82. Copyright ©2015 Pearson Education, Inc. All right reserved.

83. Copyright ©2015 Pearson Education, Inc. All right reserved.

84. Copyright ©2015 Pearson Education, Inc. All right reserved.