Solution Manual for Precalculus with Modeling and Visualization, 6th Edition

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TESTINGMANUALMATHMADEVISIBLEALGEBRA ANDTRIGONOMETRYWITHMODELING ANDVISUALIZATIONPRECALCULUS WITHMODELINGANDVISUALIZATIONSIXTHEDITIONGary RockswoldMinnesota State University, MankatowithTerry KriegerRochester Community and Technical CollegeandJessica Rockswold

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Table of ContentsChapter 1Introduction to Functions and Graphs1Chapter 2Linear Functions and Equations17Chapter 3Quadratic Functions and Equations35Chapter 4More Nonlinear Functions and Equations51Chapter 5Exponential and Logarithmic Functions69Chapter 6Trigonometric Functions85Chapter 7Trigonometric Identities and Equations103Chapter 8Further Topics in Trigonometry115Chapter 9Systems of Equations and Inequalities127Chapter 10Conic Sections147Chapter 11Further Topics in Algebra163

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1Name _______________________________RockswoldCollege Algebra & TrigonometryChapter 1 Test–Form A1. Let a functionfbe represented symbolically by2( )8.fxxFind( 1).f1._____(A)9(B)10(C)7(D)62.Determine which set of ordered pairs doesnotrepresent a function.2._____(A){(1, 1), (0, 2), (1, 3), (0, 2)}(B){(1, 1), (2, 2), (3, 3), (4, 2)}(C){(1, 4), (2, 3), (3, 1), (4, 1)}(D){(1, 1), (2, 0), (3, 1), (4, 0)}3. Use the graph offto determine its domain.3._____(A)1,(B)1, 2(C)2,(D), 4. Lake Buchanan, one of the Highland lakes located in central Texas, covers4._____1.12810square feet and contains a total volume of94.1010cubic feetof water. Find the average depth of Lake Buchanan.(A)3.66 feet(B)366 feet(C)13.6610feet(D)36.6 feet5. If possible, find the slope of the line passing through( 2.8, 6.3)and( 4.3, 1.5).5._____(A)0.3125(B)3.2(C)undefined(D)3.26. The table displays the monthly rainfall for Hilo, Hawaii, for the first six months6._____in a typical year. Find the mean rainfall to the nearest tenth of an inch forthese six months.MonthJanFebMarAprMayJunRainfall (inches)26.119.010.87.415.07.2(A)12.9 in.(B)14.3 in.(C)18.7 in.(D)85.5 in.

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Chapter 1 Test–Form ARockswoldCollege Algebra & Trigonometry27. Use the graph offto evaluate( 2).f7._____(A)1(B)2.5(C)3(D)4.88. Find the domain of1( ).4fxx8._____(A)4x(B)4,(C), 4(D), 44,9. Find the midpoint of the line segment joining the points(5.3,6.1)and( 2.8, 1.1).9._____(A)(1.25,2.5)(B)(4.05,3.6)(C)( 0.4,0.85)(D)(5.7,195)10.Find the equation of the circle.10._____(A)22(2)(1)4xy(B)22(2)(1)16xy(C)22(2)(1)4xy(D)22(2)(1)16xy11.Find the distance between the points (12.1, 13.5) and( 5.6,10.1)to the nearest tenth.11._____(A)53.8(B)29.5(C)41.3(D)9.912.Find the domain and range of the relation12._____{( 5.2, 1.6), (3.5,2.9), ( 4.9, 3.2), (6.5, 1.0), ( 2.1, 6.1)}.S(A)D{ 5.2, 1.6, 3.5,2.9,4.9}(B)D{1.6,2.9, 3.2,1.0, 6.1}R{3.2, 6.5, 1.0,2.1, 6.1}R{ 5.2, 3.5,4.9, 6.5,2.1}(C)D{ 1.5,6.0, 1.2, 9.4, 1.7}(D)D{ 5.2, 3.5,4.9, 6.5,2.1}R{4.9,1.4,6.2, 1.2, 4.1}R{1.6,2.9, 3.2,1.0, 6.1}Test Page 2

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Chapter 1 Test–Form ARockswoldCollege Algebra & Trigonometry313.In 2000 the population of Juneau, Alaska was 30,711 and in 2010 it was 31,27513._____Use the midpoint formula to estimate Juneau’s population in 2005.(A)30,183(B)30,311(C)30,366(D)30,99314.The data displayed in the table are linear. State the slopemof the line passing14._____through the data points.X10123Y85214(A)3m (B)13m(C)3m(D)13m 15.Which of the following isnotthe graph of a function?15._____16.Write a symbolic representation (formula) of a functiongthat computes16._____the number of dollars inxdimes.(A)( )10xg x(B)( )10gxx(C)( )0.10xg x(D)10( )g xx17.The functionPdefined by17._____2( )433P tttmodels the number of diagnostic machines produced by a medical equipmentmanufacturer yearly, where0tcorresponds to the first year of production, 2000.Find the average rate of change in the number of machines produced per yearbetween 2005 and 2010.(A)25 machines/year(B)17 machines/year(C)19 machines/year(D)40 machines/yearTest Page 3

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Chapter 1 Test–Form ARockswoldCollege Algebra & Trigonometry418. Plot the relation{( 3, 1), (2, 1), (5,3)}in thexy-plane.18._____19. The table shows thePizzazz-Zeecorporation’s monthly income for the first 6 months19._____of last year in thousands of dollars. Find its median monthly income for this periodto the nearest thousand dollars.MonthJanFebMarAprMayJunIncome3231292212272188(A)$185,000(B)$554,000(C)$200,000(D)$280,00020. Use the graph to determine the intervals on whichfis increasing and where it is20._____decreasing.(A)Increasing:, 53,Decreasing:3,1(B)Increasing,31, Decreasing:3,1(C)Increasing:3,Decreasing:5,(D)Increasing:1,Decreasing:3,Test Page 4

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5Name _______________________________RockswoldCollege Algebra & TrigonometryChapter 1 Test–Form B1. Let a functionfbe represented symbolically by2( )10.fxxFind( 3).f1._____(A)34(B)16(C)19(D)12. Use the graph offto determine its domain.2._____(A)6,5(B)3, 6(C), (D)2.7,5.73. If possible, find the slope of the line passing through(2.1,5.3)and(5.6,10.9).3._____(A)1.6(B)0.625(C)undefined(D)1.64. Lake Mead, formed by the construction of the Hoover Dam, covers87.59104._____square feet and contains a total volume of111.3710cubic feet of water.Find the average depth of Lake Mead.(A)180.5 feet(B)1,805 feet(C)31.80510feet(D)18.05 feet5. Determine which set of ordered pairs doesnotrepresent a function.5._____(A){(1,2), (2, 0), (3, 0), (4, 4)}(B){(1,4), (2, 0), (3, 0), (4, 2)}(C){(4, 1), (0, 2), (0, 3), (4, 4)}(D){(1, 1), (2, 0), (3, 0), (4,4)}6. The table displays the monthly rainfall for Hilo, Hawaii, for the last six months6._____in a typical year. Find the mean monthly rainfall to the nearest tenth of an inchfor these six months.MonthJulAugSepOctNovDecRainfall (inches)7.013.78.16.52.910.5(A)48.7 in.(B)7.6 in.(C)24.4 in.(D)8.1 in.

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Chapter 1 Test–Form BRockswoldCollege Algebra & Trigonometry67. Use the graph offto evaluate( 2).f7._____(A)0(B)1(C)5(D)3.38. Find the domain of1( ).5fxx8._____(A)5x(B),5(C)5,(D),55,9. Find the midpoint of the line segment joining the points( 3.1,6.5)and(6.8,3.7).9._____(A)( 4.95,1.4)(B)( 4.8, 1.55)(C)(1.7, 5.25)(D)(1.85,5.1)10. Find the equation of the circle.10._____(A)22(1)(1)25xy(B)22(1)(1)5xy(C)22(1)(1)25xy(D)22(1)(1)5xy11. Find the distance between the points( 7.3,1.47)and( 4.5, 1.47)to the nearest11._____hundredth.(A)5.74(B)16.48(C)11.80(D)4.0612. Find the domain and range of the relation12._____{(1.7,3.2), ( 3.7,2.3), ( 2.5, 3.7), (5.3, 4.1), (2.9,1.2)}.S(A)D{ 3.2,2.3, 3.7, 4.1,1.2}(B)D{1.7,3.7,2.5, 5.3, 2.9}R{1.7,3.7,2.5, 5.3, 2.9}R{ 3.2,2.3, 3.7, 4.1,1.2}(C)D{1.7,3.2,3.7,2.3,2.5}(D)D{ 1.5,6.0, 1.2, 9.4, 1.7}R{3.7, 5.3, 4.1, 2.9,1.2}R{4.9,1.4,6.2, 1.2, 4.1}Test Page 2

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Chapter 1 Test–Form BRockswoldCollege Algebra & Trigonometry713. In 2000 the population of Albuquerque, New Mexico was 448,362 and in13._____2010 it was 545,852. Use the midpoint formula to estimate Albuquerque’spopulation in 2005.(A)497,107(B)498,298(C)500,135(D)496,64114. The data displayed in the table are linear. State the slopemof the line passing14._____through the data points.X20246Y41258(A)32m (B)23m(C)23m (D)32m15. Which of the following isnotthe graph of a function?15._____16. Write a symbolic representation (formula) of a functiongthat computes the16._____number of dimes inxdollars.(A)( )0.10gxx(B)( )10xg x(C)( )10gxx(D)( )0.10xg x17. The functionPdefined by17._____2( )2.50.512P tttmodels the number of diagnostic machines produced by a medical equipmentmanufacturer yearly, where0tcorresponds to the first year of production, 2000.Find the average rate of change in the number of machines produced yearly between2005 and 2010.(A)28 machines/year(B)190 machines/year(C)38 machines/year(D)95 machines/yearTest Page 3

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Chapter 1 Test–Form BRockswoldCollege Algebra & Trigonometry818. Plot the relation{( 3, 1), ( 3,2), (5, 4)}in thexy-plane.18._____19. Use the graph to determine the intervals on whichfis increasing and which it is19._____decreasing.(A)Increasing:7, 1Decreasing:(,7) (1,) (B)Increasing:( 7,)Decreasing:(1,)(C)Increasing:0, 4Decreasing:[, 0) (4,)(D)Increasing:(0,)Decreasing:(4,)20. The table shows thePizzazz-Zeecorporation’s income for the first 6 months20._____of last year in thousands of dollars. Find its median monthly income for thisperiod to the nearest thousand dollars.MonthJanFebMarAprMayJunIncome193171257329379221(A)$239,000(B)$258,000(C)$208,000(D)$920,000Test Page 4

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9Name _______________________________RockswoldCollege Algebra & TrigonometryChapter 1 Test–Form C1. Let a functionfbe represented symbolically by2( )11.fxxFind( 5).f1.____________2. Lake Roosevelt, formed by the construction of the Grand Coulee Dam,2.____________covers83.9810square feet and contains a total volume of102.5110cubic feet of water. Find the average depth of Lake Roosevelt to the nearesttenth of a foot.3. Use the graph offto determine its domain.3.____________4. If possible, find the slope of the line passing through( 1.7,5.3)and4.____________(0.1, –9.8).5. Determine which set of ordered pairs doesnotrepresent a function.5.____________(A){(1, 2), (2, 4), (3, 0), (4, 2)}(B){(1,8), (2, 2), (3, 0), (4, 4)}(C){( 1, 1), ( 2, 2), ( 1, 3), (0, 4)}(D){(1, 4), (2, 4), (3, 4), (4, 4)}6. The table displays the monthly rainfall for Tampa, Florida, for the6.____________first six months in a typical year. Find the mean monthly rainfall to thenearest hundredth of an inch for these six months.MonthJanFebMarAprMayJunRainfall (inches)2.22.72.81.82.95.57. Use the graph offto evaluate(0).f7.____________

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Chapter 1 Test–Form CRockswoldCollege Algebra & Trigonometry108. Find the domain of( )10.fxx8.____________9. Find the midpoint of the line segment joining the points(4.1, 1.9)and9.____________(6.1, 3.5).10.Find the equation of the circle.10.____________11.Find the distance between the points(11.2,8.9)and(2.7, 11.5)to the11.____________nearest tenth.12.Find the domain and range of the relation12.____________{( 4.8,1.2), (1.5,2.7), (3.2, 5.4), (1.9, 5.1), (2.9,1.7)}.S13.In 2000 the population of Austin, Texas was 659,627 and in 2010 it was13.____________790,390. Use the midpoint formula to estimate Austin’s populationin 2005.14.The data displayed in the table are linear. State the slopemof the line14.____________passing through the data points.X42024Y13832715.Which of the following isnotthe graph of a function?15.____________Test Page 2

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Chapter 1 Test–Form CRockswoldCollege Algebra & Trigonometry1116.Write a symbolic representation (formula) of a functionfthat computes the16.____________number of ounces inxpounds.17.The functionPdefined by17.____________2( )1.52.542P tttmodels the number of diagnostic machines produced by a medicalequipment manufacturer yearly, where0tcorresponds to the first yearof production, 2000. Find the average rate of change in the numberof machines produced yearly between 2005 and 2010.18.Plot the relation{( 3, 7), ( 1, 3), ( 5,3), (8,1), (2, 2)}Sin thexy-plane.18.____________19.Use the graph to determine the intervals on whichfis increasing and19.____________on which it is decreasing.20.The table shows thePizzazz-Zeecorporation’s income for the first 6 months20.____________of last year in thousands of dollars. Find its median monthly income for thisperiod to the nearest thousand dollars.MonthJanFebMarAprMayJunIncome12793173125137149Test Page 3

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12Name _______________________________RockswoldCollege Algebra & TrigonometryChapter 1 Test–Form D1. Let a functionfbe represented symbolically by2( )12.fxxFind( 6).f1.____________2. Lake Powell, formed by the construction of the Glen Canyon Dam, covers2.____________7.78810square feet and contains a total volume of109.8410cubic feet ofwater. Find the average depth of Lake Powell to the nearest tenth of a foot.3. Use the graph offto determine its domain.3.____________4. If possible, find the slope of the line passing through(4.2,1.3)and(7.4, 3.5).4.____________5. Determine which set of ordered pairs doesnotrepresent a function.5.____________(A){(1, 2), (2, 4), (3, 6), (4, 8)}(B){(8, 4), (6, 3), (4, 2), (2, 1)}(C){( 1,), ( 2,), ( 3,), ( 4,)}(D){(, 1), (, 2), (, 3), (, 4)}6. The table displays the monthly rainfall for Tampa, Florida, for the last six months6.____________in a typical year. Find the mean monthly rainfall to the nearest hundredth ofan inch for these six months.MonthJulAugSepOctNovDecRainfall (inches)6.47.66.52.41.62.37. Use the graph offto evaluate(2).f7.____________8. Find the domain of( )8.fxx8.____________9. Find the midpoint of the line segment joining the points( 1.3, 5.7)9.____________and (4.6, 2.1).

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Chapter 1 Test–Form DRockswoldCollege Algebra & Trigonometry1310. Find the equation of the circle.10.____________11. Find the distance between the points (1.81. 8.13) and( 5.11, 2.94)to the11.____________nearest hundredth.12. Find the domain and range of the relation12.____________{(4.8, 2.1), (5.2, 1.9), ( 1.7,4.3), (2.2,3.9), ( 4.9,1.1)}.S13. In 2000 the population of Portland, Oregon was 529,209 and in 2010 it13.____________was 583,776. Use the midpoint formula to estimate Portland’s populationin 2005.14. The data displayed in the table are linear. State the slopemof the line14.____________passing through the data points.X95137Y3210115. Which of the following isnotthe graph of a function?15.____________16. Write a symbolic representation (formula) of a functionfthat computes the16.____________number of pounds inxounces.Test Page 2

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