Concept Explanation Examples Distance formula The distance between (x 1, y 1 ) and (x 2, y 2 ) is d = 2(x 2 - x 1 ) 2 + ( y 2 - y 1 ) 2.

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1 660_ch0pp qd 0/6/08 4:8 PM Page 4 4 CHAPTER Introduction to Functions and Graphs continued from previous page Concept Eplanation Eamples Distance formula The distance between (, y ) and (, y ) is d = ( - ) + ( y - y ). The distance between (, -) and (-, ) is d = (- - ) + ( - (-)) = 5. Midpoint formula The midpoint of the line segment connecting (, y ) and (, y ) is M = a +, y + y b. The midpoint of the line segment connecting (4, ) and (-, 5) is M = a 4 + (-), + 5 b = (, 4). Standard equation of a circle The circle with center (h, k) and radius r The circle with center (-, 4) and radius 5 has the has the equation equation ( - h) + ( y - k) = r. ( + ) + ( y - 4) = 5. The net table summarizes some basic concepts related to one-variable and two-variable data. Type of Data Methods of Visualization Comments One-variable data Number line, list, one-column or one-row table The data items are the same type and can be described using -values. Computations of the mean and median are performed on one-variable data. Two-variable data Two-column or two-row table, scatterplot, line graph or other type of graph in the y-plane Two types of data are related and can be described by using ordered pairs (, y).. Eercises Data Involving One Variable Eercises 4: For the table of data, complete the following. (a) Plot the numbers on a number line. (b) Find the maimum and minimum of the data. (c) Determine the mean of the data Eercises 5 8: Sort the list of numbers from smallest to largest and display the result in a table. (a) Determine the maimum and minimum values. ( b) Calculate the mean and median. Round each result to the nearest hundredth when appropriate , 5, 5, -0, 55, 6, -0, 45, , 4.75, -.5,.5,.5, 4.75, ,., 69, p, p, ,.4, 8, 9.4, 4 0.9,.

2 660_ch0pp qd 0/6/08 4:8 PM Page 5. Eercises 9 and 0: Geography The set of numbers contains data about geographic features of the world. (a) Plot the numbers on a number line. (b) Calculate the mean and median for the set of numbers. Interpret your results. (c) Try to identify the geographic feature associated with the largest number in the set. 9. {.7,.,., 6.8, 4.9,.0} (Areas of largest freshwater lakes in thousands of square miles) (Source: U.S. National Oceanic and Atmospheric Administration.) 0. {9., 8.5, 9.0, 7., 6.,.8, 0.} (Highest elevations of the continents in thousands of feet) (Source: National Geographic Atlas of the World.). Designing a Data Set Find a set of three numbers with a mean of 0 and a median of 8. Is your answer unique?. Designing a Data Set Find a set of five numbers with a mean of 0 and a median of 9. Is your answer unique? Distance Formula Eercises 8: Find the eact distance between the two points. Where appropriate, also give approimate results to the nearest hundredth.. (, - ), (5, ) 4. (0, -), (, -8) 5. (7, -4 ), (9, ) 6. ( -, -6), ( -8, -5) 7. (.6, 5.7), (-., 8.7) 8. ( -6.5,.7), (.6, -.9) 9. ( -, ), (-, 0) 0. (7, 9), ( -, 9). A, - B, A4, B. A -, B, A, - 4B 5. (0, 0), (-0, -90 ) 6. (40, 6), (-0, 7) 7. (a, 0), (0, -b ) 8. (, y), (, ) 4 B, A - 0, 5B. A5, 0 Visualizing and Graphing Data 5 (a) Let (0, 0) be the initial coordinates of car B in the y-plane, where units are in miles. Plot the locations of each car at 9:00 A.M. and at :00 A.M. (b) Find the distance d between the cars at :00 A.M.. Distance between Ships Two ships leave a harbor at the same time. The first ship heads north at 0 miles per hour, and the second ship heads west at 5 miles per hour. Write an epression that gives the distance d between the ships after t hours. Midpoint Formula Eercises 6: Use the midpoint formula for the following.. U.S. Average Life Epectancy The average life epectancy for a female born in the United States was 77.4 years in 980 and 79.5 years in 000. Estimate the average life epectancy for a female born in 990. (Actual life epectancy was 78.8.) (Source: Bureau of the Census.) 4. State and Federal Inmates In 990 there were 77,99 inmates in state and federal prisons, and in 000 there were,9,89. Estimate the number of inmates in 995. (Actual number was,5,874.) (Source: Department of Justice.) 5. Olympic Times In the Olympic Games, the 00-meter dash is run in approimately 0 seconds. Estimate the time to run the 00-meter dash. 4. A -, B, A, - 5B 9. Geometry An isosceles triangle has at least two sides of equal length. Determine whether the triangle with vertices (0, 0), (, 4), (7, ) is isosceles. 0. Geometry An equilateral triangle has sides of equal length. Determine whether the triangle with vertices (-, -), (, ), ( -4, ) is equilateral.. Distance between Cars (Refer to Eample 6.) At 9:00 A.M. car A is traveling north at 50 miles per hour and is located 50 miles south of car B. Car B is traveling west at 0 miles per hour. 6. Real Numbers Between any two real numbers a and b there is always another real number. How could such a number be found? Eercises 7 46: Find the midpoint of the line segment connecting the points. 7. (, ), (5, -) 8. ( -6, 7), (9, -4) 9. ( -0, 50), (50, -0) 40. (8, -), (5, 8)

3 660_ch0pp qd 0/6/08 4:8 PM Page 6 6 CHAPTER Introduction to Functions and Graphs 4. (.5,.9), (-5.7, -.6) 4. (9.4, -4.5), (-7.7, 9.5) 4. (, 5), (, - 5) 44. (7, ), (-7, -) 45. (a, b), (-a, b) 46. (-a, b), (a, b) Data Involving Two Variables Eercises 47 50: For the table of data, complete the following. (a) Epress the data as a relation S. (b) Find the domain and range of S y y y y Eercises 5 56: Complete the following. (a) Find the domain and range of the relation. (b) Determine the maimum and minimum of the -values and then of the y-values. (c) Label appropriate scales on the y-aes. (d) Plot the relation. 5. {(0, 5), (-, 4), (-, -5), (7, -), (0, 0)} {(, ), (, 0), (-5, -5), (8, -), (0, )} {(, ), (-, ), (-4, -), (-, ), (0, -)} {(, ), (, -), (-, -), (-, ), (-, 0)} {(0, 50), (-5, 45), (0, -55), (75, 5), (-5, -5)} {(-.,.5), (.0, 0.5), (-0.,.), (-0.8, -.)} Eercises 57 and 58: Plotting Real Data Use the table to make a scatterplot and line graph of the data. 57. Cell phone subscribers (millions) Year Subscribers Source: CTIA The Wireless Association. 58. Atmospheric CO levels (parts per million) Circles Eercises 59 66: Find the center and radius of the circle y = y = y = y = ( - ) + ( y + ) = 9 ( + ) + ( y - ) = ( y + ) = ( - 5) + y = 9 Eercises 67 70: Find the standard equation of the circle. 67. y 68. y y Eercises 7 78: Find the standard equation of a circle that satisfies the conditions. 7. Radius 8, center (, -5) 7. Radius 5, center (-, 4) Year CO amounts Source: Mauna Loa Observatory. 7. Radius 7, center (, 0) 74. Radius, center (0, 0) 75. Center (0, 0) with the point (-, -) on the circle 6 y

4 660_ch0pp qd 0/6/08 4:8 PM Page 7. Visualizing and Graphing Data Center (, -5) with the point (4, ) on the circle 9. {(0, -0), (-40, 50), (0, 60), (-50, -80), (70, 0)} 77. Endpoints of a diameter (-5, -7) and (, ) 78. Endpoints of a diameter (-, -) and (, - 4) Graphing Calculators Eercises 79 84: Predict the number of tick marks on the positive -ais and the positive y-ais. Then show the viewing rectangle on your graphing calculator. 79. Standard viewing rectangle 80. [-4.7, 4.7, ] by [-.,., ] 8. [0, 00, 0] by [-50, 50, 0] 8. [-0, 0, 5] by [-0, 0, 5] 8. [980, 995, ] by [000, 6000, 000] 84. [800, 000, 0] by [5, 0, 5] Eercises 85 88: Match the settings for a viewing rectangle with the correct figure (a d). 85. [-9, 9, ] by [-6, 6, ] 86. [-6, 6, ] by [-9, 9, ] 87. [-,, 0.5] by [-4.5, 4.5, 0.5] 88. [-4, 8, ] by [-600, 600, 00] a. b. 9. {(-., 0.6), (.0, -0.5), (0.4, 0.), (-.8,.4)} Eercises 9 96: The table contains real data. (a) Determine the maimum and minimum values for each variable in the table. (b) Use your results from part (a) to find an appropriate viewing rectangle. (c) Make a scatterplot of the data. (d) Make a line graph of the data. 9. Digital subscriber lines (millions) Year DSL users Source: Federal Communications Commission. 94. Cable modems (millions) Year Modems Source: Federal Communications Commission. 95. Worldwide cigarette sales (trillions) Year Cigarettes Source: Department of Agriculture. 96. Asian-American population y (in millions) during year y Source: U.S. Census Bureau. c. d. Eercises 89 9: Make a scatterplot of the relation. 89. {(, ), (-, ), (-4, ), (-, -4), (0, )} Writing about Mathematics 97. Give an eample of a relation that has meaning in the real world. Give an eample of an ordered pair (, y) that is in your relation. Does the ordered pair (y, ) also have meaning? Eplain your answers. 98. Do the mean and median represent the same thing? Eplain your answer and give an eample. 90. {(6, 8), (-4, -0), (-, -6), (, -5)}

5 660_ch0pp qd 0/6/08 4:8 PM Page 8 8 CHAPTER Introduction to Functions and Graphs CHECKING BASIC CONCEPTS FOR SECTIONS. AND.. Approimate each epression to the nearest hundredth (a) 4.( ) (b) Evaluate the epression by hand. (a) 5 - (-4) # (b) 5, 5 +. Write each number using scientific notation. (a) 48,500,000 (b) -7.4 (c) Find the eact distance between the points (-, ) and (, -5). Then round this distance to the nearest hundredth. 5. Find the midpoint of the line segment connecting the points (-, ) and (4, ). 6. Find the standard equation of a circle with center and radius 8. (-4, 5) 7. The average depths in feet of the four oceans are,5,,88,,00, and 95. Calculate the mean and median of these depths. 8. Make a scatterplot and a line graph with the four points (-5, -4), (-, ), (, -), and (, 6). State the quadrant in which each point lies.. Functions and Their Representations Learn function notation Represent a function four different ways Define a function formally Identify the domain and range of a function Use calculators to represent functions (optional) Identify functions Represent functions with diagrams and equations Introduction Because there are more than 00 million people in the United States who consume many natural resources, going green has become an important social and environmental issue. Collectively, we affect the world around us. The average person uses 00 paper napkins a year. A washing machine uses about 40 gallons of water for each load of clothes, and a car puts 9.4 pounds of carbon dioide into the atmosphere every time it burns a gallon of gasoline. See Eercises 99 and 00. The mathematical concept of a function includes formulas, graphs, tables, and verbal descriptions. All of these representations can be used to analyze the impact of human consumption on the environment and also to describe natural phenomena, such as lightning. This section introduces the important concept of a function, which is used throughout the course. Basic Concepts Although thunder is caused by lightning, we sometimes see a flash of lightning before we hear the thunder. This is because light travels at 86,000 miles per second, whereas sound travels at about 050 feet per second. Since mile equals 580 feet, sound takes about 5 seconds to travel mile. It follows that the farther away lightning is, the greater the time lapse between seeing the flash of lightning and hearing the thunder. Table.6 lists the approimate distance y in miles between a person and a bolt of lightning when there is a time lapse of seconds between seeing the lightning and hearing the thunder. Note that the value of y can be found by dividing the corresponding value of by 5. Table.6 Distance from Lightning (seconds) y (miles) 4 5