SECTION 3.1 |
Functions |
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Expressing a Function | |||||||||
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SECTION 3.1 |
EXERCISES |
SKILLS |
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4. |
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6. |
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8. |
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10. |
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12. |
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18. |
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22. |
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24. |
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26. |
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27. |
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28. |
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29. |
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30. |
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31. |
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32. |
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33. |
Find if in Exercise 25.
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34. | Find if in Exercise 26.
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35. |
Find if in Exercise 27.
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36. | Find if in Exercise 29.
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37. |
Find if in Exercise 29.
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38. | Find if in Exercise 30.
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39. |
Find if in Exercise 31.
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40. | Find if in Exercise 32.
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41. |
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42. |
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44. |
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46. |
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48. |
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50. |
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52. |
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54. |
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56. |
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58. |
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60. |
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62. |
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64. |
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66. |
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68. |
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70. |
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72. |
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74. |
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76. |
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78. |
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80. |
81. |
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82. |
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84. |
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86. |
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88. |
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90. |
91. |
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92. |
93. |
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94. |
95. |
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96. |
97. |
Let and find the values of that correspond to .
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98. | Let and find the value of that corresponds to .
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99. |
Let and find the values of that correspond to .
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100. | Let and find the values of that correspond to .
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APPLICATIONS |
101. |
Budget: Event Planning.
The cost associated with a catered wedding reception is per person for a reception for more than 75 people. Write the cost of the reception in terms of the number of guests and state any domain restrictions.
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102. |
Budget: Long-Distance Calling.
The cost of a local home phone plan is for basic service and per minute for any domestic long-distance calls. Write the cost of monthly phone service in terms of the number of monthly long-distance minutes and state any domain restrictions.
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103. |
Temperature.
The average temperature in Tampa, Florida, in the springtime is given by the function , where is the temperature in degrees Fahrenheit and is the time of day in military time and is restricted to (sunrise to sunset). What is the temperature at 6 a.m.? What is the temperature at noon?
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104. |
Falling Objects: Firecrackers.
A firecracker is launched straight up, and its height is a function of time, , where is the height in feet and is the time in seconds with corresponding to the instant it launches. What is the height 4 seconds after launch? What is the domain of this function?
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105. |
Collectibles.
The price of a signed Alex Rodriguez baseball card is a function of how many are for sale. When Rodriguez was traded from the Texas Rangers to the New York Yankees in 2004, the going rate for a signed baseball card on eBay was , where represents the number of signed cards for sale. What was the value of the card when there were 10 signed cards for sale? What was the value of the card when there were 100 signed cards for sale?
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106. |
Collectibles.
In Exercise 105, what was the lowest price on eBay, and how many cards were available then? What was the highest price on eBay, and how many cards were available then?
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107. |
Volume.
An open box is constructed from a square 10-inch piece of cardboard by cutting squares of length inches out of each corner and folding the sides up. Express the volume of the box as a function of , and state the domain.
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108. |
Volume.
A cylindrical water basin will be built to harvest rainwater. The basin is limited in that the largest radius it can have is . Write a function representing the volume of water as a function of height . How many additional gallons of water will be collected if you increase the height by ?
Hint: .
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109. |
Economics.
Approximate the exchange rates of the U.S. dollar to the nearest yen during Weeks 4, 7, and 8.
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110. |
Economics.
Find the increase or decrease in the number of Japanese yen to the U.S. dollar exchange rate, to the nearest yen, from (a) Week 2 to Week 3 and (b) Week 6 to Week 7.
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111. |
Medicine/Health.
How many people have contracted malaria 14 days into the outbreak?
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112. |
Medicine/Health.
How many people have contracted malaria 6 days into the outbreak?
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113. |
Environment: Tossing the Envelopes.
The average American adult receives 24 pieces of mail per week, usually of some combination of ads and envelopes with windows. Suppose each of these adults throws away a dozen envelopes per week.
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114. |
Environment: Tossing the Envelopes.
Each month, Jack receives his bank statement in a 9.5 inch by 6 inch envelope. Each month, he throws away the envelope after removing the statement.
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115. |
Finance.
Is the relation whose domain is the year and whose range is the average federal funds rate for the month of January a function? Explain.
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116. |
Finance.
Write five ordered pairs whose domain is the set of even years from 2000 to 2008 and whose range is the set of corresponding average federal funds rate for the month of January.
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117. |
Health Care Costs.
Fill in the following table. Round dollars to the nearest .
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118. |
Health Care Costs.
Using the table found in Exercise 117, let the years correspond to the domain and the total costs correspond to the range. Is this relation a function? Explain.
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119. |
Environment: Global Climate Change.
Estimate (to the nearest thousand) the value of
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120. |
Environment: Global Climate Change.
Explain what the sum represents.
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CATCH THE MISTAKE |
121. |
Determine whether the relationship is a function.
Solution:
Apply the horizontal line test.
Because the horizontal line intersects the graph in two places, this is not a function.
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122. |
Given the function , evaluate the quantity .
Solution:
This is incorrect. What mistake was made?
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123. |
Given the function , evaluate the quantity .
Solution:
This is incorrect. What mistake was made?
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124. |
Determine the domain of the function and express it in interval notation.
Solution:
What can be? Any nonnegative real number.
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125. |
Given the function , evaluate .
Solution:
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126. |
Given the functions and , find .
Solution:
This is incorrect. What mistake was made?
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CONCEPTUAL |
127. |
If a vertical line does not intersect the graph of an equation, then that equation does not represent a function. |
128. | If a horizontal line intersects a graph of an equation more than once, the equation does not represent a function. |
129. |
If , then does not represent a function. |
130. | If , then may or may not represent a function. |
131. |
If and , find . |
132. | If and is undefined, find . |
CHALLENGE |
133. |
If is undefined, and , find and .
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134. | Construct a function that is undefined at and whose graph passes through the point .
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135. |
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136. |
TECHNOLOGY |
137. |
Using a graphing utility, graph the temperature function in Exercise 103. What time of day is it the warmest? What is the temperature? Looking at this function, explain why this model for Tampa, Florida, is valid only from sunrise to sunset (6 to 18).
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138. | Using a graphing utility, graph the height of the firecracker in Exercise 104. How long after liftoff is the firecracker airborne? What is the maximum height that the firecracker attains? Explain why this height model is valid only for the first 8 seconds.
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139. |
140. | The makers of malted milk balls are considering increasing the size of the spherical treats. The thin chocolate coating on a malted milk ball can be approximated by the surface area, . If the radius is increased 3 mm, what is the resulting increase in required chocolate for the thin outer coating?
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141. |
Let . Graph and in the same viewing window. Describe how the graph of can be obtained from the graph of .
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142. | Let . Graph and in the same viewing window. Describe how the graph of can be obtained from the graph of .
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Copyright © 2013 John Wiley & Sons, Inc. All rights reserved. |