Test Bank for Precalculus Enhanced with Graphing Utilities, 6th Edition

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Ch.1Graphs1.1TheDistanceandMidpointFormulas;GraphingUtilities;IntroductiontoGraphingEquations1UsetheDistanceFormulaMULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.Findthedistanced(P1,P2)betweenthepointsP1 andP2.1)x-6-4-2246y642-2-4-6x-6-4-2246y642-2-4-6A)5B) 4C)13D) 62)x-8-6-4-22468y8642-2-4-6-8x-8-6-4-22468y8642-2-4-6-8A)85B)13C) 1D) 42Page1

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3)x-8-6-4-22468y8642-2-4-6-8x-8-6-4-22468y8642-2-4-6-8A) 2B) 123C) 12D) 254)x-8-6-4-22468y8642-2-4-6-8x-8-6-4-22468y8642-2-4-6-8A) 108B) 6C) 65D) 10835) P1=(5,5);P2=(5,2)A) 2B) 4C) 3D)36) P1=(1,3);P2=(-2,-1)A) 5B) 6C) 10D) 257) P1=(0,-1);P2=(-8,-1)A)65B) 64C) 8D) 18) P1=(0,0);P2=(5,8)A) 210B) 89C)89D) 139) P1=(4,4);P2=(-6,-5)A) 1B) 90C)19D)18110) P1=(2,-6);P2=(4,-2)A) 12B) 123C) 2D) 25Page2

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11) P1=(-1,-4);P2=(4,6)A) 75B) 55C) 753D) 512) P1=(0.9,-0.6);P2=(2.7,-1.9)Roundtothreedecimalplaces,ifnecessary.A) 7.021B) 2.22C) 15.5D) 2.32Decidewhetherornotthepointsaretheverticesofarighttriangle.13) (-9,-1),(-4,-1),(-4,7)A) YesB) No14) (6,1),(8,5),(10,4)A) YesB) No15) (10,12),(16,14),(15,9)A) YesB) No16) (-3,-1),(3,1),(9,-6)A) YesB) NoSolvetheproblem.17) Findallvaluesofksothatthegivenpointsare29unitsapart.(-5,5),(k,0)A)-3,-7B)-7C) 7D) 3,718) FindtheareaoftherighttriangleABCwithA=(-2,7),B=(7,-1),C=(3,9).A) 58squareunitsB) 29squareunitsC)582squareunitsD)292squareunits19) Findallthepointshavinganx-coordinateof9whosedistancefromthepoint(3,-2)is10.A) (9,2),(9,-4)B) (9,13),(9,-7)C) (9,6),(9,-10)D) (9,-12),(9,8)20) Amiddleschoolʹsbaseballplayingfieldisasquare,65 feetonaside.Howfarisitdirectlyfromhomeplatetosecondbase(thediagonalofthesquare)?Ifnecessary,roundtothenearestfoot.A) 99feetB) 92feetC) 91 feetD) 93feet21) Amotorcycleandacarleaveanintersectionatthesametime.Themotorcycleheadsnorthatanaveragespeedof20milesperhour,whilethecarheadseastatanaveragespeedof48milesperhour.Findanexpressionfortheirdistanceapartinmilesattheendofthours.A) 52tmilesB) t68milesC) 2t13milesD) 52tmiles22) Arectangularcityparkhasajoggingloopthatgoesalongalength,width,anddiagonalofthepark.Tothenearestyard,findthelengthofthejoggingloop,ifthelengthoftheparkis125yardsanditswidthis75yards.A) 346yardsB) 145yardsC) 345yardsD) 146yardsPage3

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23) FindthelengthofeachsideofthetriangledeterminedbythethreepointsP1,P2,andP3.Statewhetherthetriangleisanisoscelestriangle,arighttriangle,neitherofthese,orboth.P1=(-5,-4),P2=(-3,4),P3=(0,-1)A) d(P1,P2)=217;d(P2,P3)=34;d(P1,P3)=52righttriangleB) d(P1,P2)=217;d(P2,P3)=34;d(P1,P3)=52neitherC) d(P1,P2)=217;d(P2,P3)=34;d(P1,P3)=34bothD) d(P1,P2)=217;d(P2,P3)=34;d(P1,P3)=34isoscelestriangle2UsetheMidpointFormulaMULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.FindthemidpointofthelinesegmentjoiningthepointsP1 andP2.1) P1=(1,5);P2=(9,3)A) (-8,2)B) (10,8)C) (5,4)D) (4,5)2) P1=(4,4);P2=(7,-7)A) 11,-3B)-32 ,112C)-3,11D)112 ,-323) P1=(7,1);P2=(-16,-16)A) 9,15B)232 ,172C)-92 ,-152D)-9,-154) P1=(-0.7,0.1);P2=(1.8,-2.1)A) (-1.1,1.25)B) (0.55,-1)C) (-1,0.55)D) (1.25,-1.1)5) P1=(a,3);P2=(0,9)A) a,12B)-a2 ,6C)a,6D)a2 ,66) P1=(5b,9);P2=(6b,4)A) b,5B)11b2,132C)11b,13D)13b2,112Solvetheproblem.7) If(-3,1)istheendpointofalinesegment,and(2,4)isitsmidpoint,findtheotherendpoint.A) (7,-2)B) (3,11)C) (7,7)D) (-13,-5)8) If(4,5)istheendpointofalinesegment,and(2,1)isitsmidpoint,findtheotherendpoint.A) (-4,1)B) (8,13)C) (0,9)D) (0,-3)9) If(-1,-10)istheendpointofalinesegment,and(2,-12)isitsmidpoint,findtheotherendpoint.A) (-7,-6)B) (-5,-4)C) (5,-14)D) (5,-8)10) If(5,-3)istheendpointofalinesegment,and(1,-2)isitsmidpoint,findtheotherendpoint.A) (-3,-4)B) (13,-5)C) (7,-11)D) (-3,-1)Page4

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11) Themediansofatriangleintersectatapoint.Thedistancefromthevertextothepointisexactlytwo-thirdsofthedistancefromthevertextothemidpointoftheoppositeside.FindtheexactdistanceofthatpointfromthevertexA(3,4)ofatriangle,giventhattheothertwoverticesareat(0,0)and(8,0).A) 83B)173C) 2D) 21733GraphEquationsbyHandbyPlottingPointsMULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.Plotthepointinthexy-plane.Tellinwhichquadrantoronwhataxisthepointlies.1) (6,2)x-55y5-5x-55y5-5A)x-55y5-5x-55y5-5QuadrantIIB)x-55y5-5x-55y5-5QuadrantIC)x-55y5-5x-55y5-5QuadrantIVD)x-55y5-5x-55y5-5QuadrantIPage5

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2) (-2,6)x-55y5-5x-55y5-5A)x-55y5-5x-55y5-5QuadrantIVB)x-55y5-5x-55y5-5QuadrantIC)x-55y5-5x-55y5-5QuadrantIIID)x-55y5-5x-55y5-5QuadrantIIPage6

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3) (1,-3)x-55y5-5x-55y5-5A)x-55y5-5x-55y5-5QuadrantIVB)x-55y5-5x-55y5-5QuadrantIIC)x-55y5-5x-55y5-5QuadrantID)x-55y5-5x-55y5-5QuadrantIIIPage7

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4) (-5,-3)x-55y5-5x-55y5-5A)x-55y5-5x-55y5-5QuadrantIIIB)x-55y5-5x-55y5-5QuadrantIVC)x-55y5-5x-55y5-5QuadrantIIID)x-55y5-5x-55y5-5QuadrantIIPage8

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5) (0,-4)x-55y5-5x-55y5-5A)x-55y5-5x-55y5-5QuadrantIIB)x-55y5-5x-55y5-5x-axisC)x-55y5-5x-55y5-5y-axisD)x-55y5-5x-55y5-5y-axisPage9

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6) (5,0)x-55y5-5x-55y5-5A)x-55y5-5x-55y5-5x-axisB)x-55y5-5x-55y5-5x-axisC)x-55y5-5x-55y5-5QuadrantIID)x-55y5-5x-55y5-5y-axisDeterminewhetherthegivenpointisonthegraphoftheequation.7) Equation:y=x4-xPoint:(4,254)A) YesB) No8) Equation:x2+y2=64Point:(8,0)A) YesB) NoPage10

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Graphtheequationbyplottingpoints.9) y=x+5x-10-5510y105-5-10x-10-5510y105-5-10A)x-10-5510y105-5-10x-10-5510y105-5-10B)x-10-5510y105-5-10x-10-5510y105-5-10C)x-10-5510y105-5-10x-10-5510y105-5-10D)x-10-5510y105-5-10x-10-5510y105-5-10Page11

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10) y=3x+6x-10-5510y105-5-10x-10-5510y105-5-10A)x-10-5510y105-5-10x-10-5510y105-5-10B)x-10-5510y105-5-10x-10-5510y105-5-10C)x-10-5510y105-5-10x-10-5510y105-5-10D)x-10-5510y105-5-10x-10-5510y105-5-10Page12

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11) y=x2-1x-10-5510y105-5-10x-10-5510y105-5-10A)x-10-5510y105-5-10x-10-5510y105-5-10B)x-10-5510y105-5-10x-10-5510y105-5-10C)x-10-5510y105-5-10x-10-5510y105-5-10D)x-10-5510y105-5-10x-10-5510y105-5-10Page13

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12) 3x+5y=15x-10-5510y105-5-10x-10-5510y105-5-10A)x-10-5510y105-5-10x-10-5510y105-5-10B)x-10-5510y105-5-10x-10-5510y105-5-10C)x-10-5510y105-5-10x-10-5510y105-5-10D)x-10-5510y105-5-10x-10-5510y105-5-10Page14

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13) 4x2+y=4x-10-5510y105-5-10x-10-5510y105-5-10A)x-10-5510y105-5-10x-10-5510y105-5-10B)x-10-5510y105-5-10x-10-5510y105-5-10C)x-10-5510y105-5-10x-10-5510y105-5-10D)x-10-5510y105-5-10x-10-5510y105-5-10Page15

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4GraphEquationsUsingaGraphingUtilityMULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.Determinethecoordinatesofthepointshown.Tellinwhichquadrantthepointlies.Assumethecoordinatesareintegers.1)A) (-4,6);quadrantIB) (-4,6);quadrantIIC) (-4,3);quadrantIID) (-4,3);quadrantISelectasettingsothateachofthegivenpointswilllieintheviewingwindow.2) (8,3),(5,1),(9,19)A)B)C)D)Page16

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Determinetheviewingwindowused.3)A)B)C)D)Page17

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Graphtheequationusingagraphingutility.4) y=2x+1A)B)C)D)5) 2x-3y=3A)B)C)D)Page18

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6) y=-2x2+9A)B)C)D)7) 3x2-2y=56A)B)C)D)Page19

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5UseaGraphingUtilitytoCreateTablesMULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.Useagraphingutilitytocreateatablethatdisplaysthepointsonthegraphofthegivenequationforx= -3,-2,-1,0,1,2,and3.1) y=3x+5A)B)C)D)2) 6x+2y=28A)B)C)D)Page20

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3) y=-3x2+10A)B)C)D)4) 4x2-2y=16A)B)C)D)Page21

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6FindInterceptsfromaGraphMULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.Listtheinterceptsofthegraph.1)x-10-5510y105-5-10x-10-5510y105-5-10A) (0,-2),(2,0)B) (-2,0),(0,2)C) (0,-2),(0,2)D) (-2,0),(2,0)2)x-55y5-5x-55y5-5A) (0,1)B) (1,1)C) (1,0)D) (0,0)Page22

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3)x-π-π2π2πy54321-1-2-3-4-5x-π-π2π2πy54321-1-2-3-4-5A) 0,-π2 ,(0,-3),0,π2B)-π2 ,0 ,(0,-3),π2 ,0C)0,-π2 ,(-3,0),0,π2D)-π2 ,0 ,(-3,0),π2 ,04)x-10-5510y105-5-10x-10-5510y105-5-10A) (0,-4),(8,0),(0,2)B) (0,-4),(0,8),(2,0)C) (-4,0),(0,8),(0,2)D) (-4,0),(0,8),(2,0)5)x-10-5510y105-5-10x-10-5510y105-5-10A) (0,-2)B) (-2,0)C) (2,0)D) (0,2)Page23

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6)x-10-5510y105-5-10x-10-5510y105-5-10A) (-3,0),(0,3)B) (-3,0),(0,-3),(0,0),(0,3),(3,0)C) (0,3),(3,0)D) (-3,0),(0,-3),(0,3),(3,0)7)x-10-5510y105-5-10x-10-5510y105-5-10A) (4,0),(0,4),(0,1),(0,-5)B) (4,0),(0,-4),(0,1),(0,5)C) (4,0),(1,0),(-5,0),(0,4)D) (-4,0),(1,0)(5,0),(0,4)8)A) (-2,0),(2,0)B) (-2,0),(0,2),(2,0)C) (-2,0),(0,4),(2,0)D) (-4,0),(0,4),(4,0)Page24

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7UseaGraphingUtilitytoApproximateInterceptsMULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.Graphtheequationusingagraphingutility.Useagraphingutilitytoapproximatetheinterceptsroundedtotwodecimalplaces,ifnecessary.UsetheTABLEfeaturetohelpestablishtheviewingwindow.1) y=-2x+15A) (0,-15),(7.5,0)B) (0,15),(-7.5,0),(7.5,0)C) (0,15),(7.5,0)D) (0,15),(-7.5,0)2) y=-4x+15A) (0,-3.75),(15,0)B) (0,3.75),(15,0)C) (0,15),(-3.75,0)D) (0,15),(3.75,0)3) y=3x2-19A) (0,-19),(-2.51,0),(2.51,0)B) (0,19),(-2.52,0),(2.52,0)C) (0,-19),(2.52,0)D) (0,-19),(-2.52,0),(2.52,0)4) y=5x2-13A) (0,1.61),(0,-1.61),(-13,0)B) (0,-13),(2.60,0),(-2.60,0)C) (0,-13),(1.61,0),(-1.61,0)D) (0,2.60),(0,-2.60),(-13,0)5) 3x-4y=56A) (0,14),(18.67,0)B) (0,-14),(-18.67,0),(18.67,0)C) (0,-14),(18.66,0)D) (0,-14),(18.67,0)6) 6x-5y=67A) (0,11.17),(-13.40,0)B) (0,13.40),(-11.17,0)C) (0,-13.41),(11.18,0)D) (0,-13.40),(11.17,0)7) 3x2-5y=34A) (0,-6.8),(3.37,0)B) (0,-6.8),(-3.36,0),(3.36,0)C) (0,-6.8),(-3.37,0),(3.37,0)D) (0,6.8),(-3.37,0),(3.37,0)8) 4x2-5y=68A) (0,-13.60),(4.12,0),(-4.12,0)B) (0,13.60),(4.12,0),(-4.12,0)C) (0,4.12),(0,-4.12),(-13.60,0)D) (0,-13.59),(4.13,0),(-4.13,0)1.2Intercepts;Symmetry;GraphingKeyEquations1FindInterceptsfromanEquationMULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.Listtheinterceptsforthegraphoftheequation.1) y=x+6A) (-6,0),(0,6)B) (6,0),(0,-6)C) (6,0),(0,6)D) (-6,0),(0,-6)2) y=-4xA) (0,-4)B) (0,0)C) (-4,0)D) (-4,-4)3) y2=x+1A) (0,-1),(1,0),(0,1)B) (1,0),(0,1),(0,-1)C) (-1,0),(0,-1),(1,0)D) (0,-1),(-1,0), (0,1)Page25

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4) y=9 xA) (1,0)B) (0,0)C) (0,1)D) (1,1)5) x2+y-9=0A) (0,-3),(9,0),(0,3)B) (-3,0),(0,9), (3,0)C) (3,0),(0,9),(0,-9)D) (-3,0),(0,-9), (3,0)6) 4x2+9y2=36A) (-4,0),(-9,0),(9,0),(4,0)B) (-3,0),(0,-2),(0,2),(3,0)C) (-2,0),(-3,0),(3,0),(2,0)D) (-9,0),(0,-4),(0,4),(9,0)7) 4x2+y2=4A) (-4,0),(0,-1),(0,1),(4,0)B) (-1,0),(0,-4),(0,4),(1,0)C) (-1,0),(0,-2),(0,2),(1,0)D) (-2,0),(0,-1),(0,1),(2,0)8) y=x3-8A) (0,-2),(-2,0)B) (0,-8),(2,0)C) (0,-2),(0,2)D) (-8,0),(0,2)9) y=x4-1A) (0,1)B) (0,-1)C) (0,-1),(-1,0),(1,0)D) (0,1),(-1,0),(1,0)10) y=x2+11x+24A) (-3,0),(-8,0),(0,24)B) (0,-3),(0,-8),(24,0)C) (3,0),(8,0),(0,24)D) (0,3),(0,8),(24,0)11) y=x2+4A) (4,0)B) (0,4)C) (0,4),(-2,0),(2,0)D) (4,0),(0,-2),(0,2)12) y=9xx2+81A) (-81,0),(0,0),(81,0)B) (0,0)C) (0,-9),(0,0),(0,9)D) (-9,0),(0,0),(9,0)13) y=x2-93x4A) (0,-3),(0,3)B) (-3,0),(3,0)C) (0,0)D) (-9,0),(0,0),(9,0)Page26

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2TestanEquationforSymmetryMULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.PlotthepointA.PlotthepointBthathasthegivensymmetrywithpointA.1) A=(4,-4);BissymmetrictoAwithrespecttothey-axisx-5-4-3-2-112345y54321-1-2-3-4-5x-5-4-3-2-112345y54321-1-2-3-4-5A)x-5-4-3-2-112345y54321-1-2-3-4-5ABx-5-4-3-2-112345y54321-1-2-3-4-5ABB)x-5-4-3-2-112345y54321-1-2-3-4-5ABx-5-4-3-2-112345y54321-1-2-3-4-5ABC)x-5-4-3-2-112345y54321-1-2-3-4-5ABx-5-4-3-2-112345y54321-1-2-3-4-5ABD)x-5-4-3-2-112345y54321-1-2-3-4-5ABx-5-4-3-2-112345y54321-1-2-3-4-5ABPage27

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2) A=(0,5);BissymmetrictoAwithrespecttotheoriginx-5-4-3-2-112345y54321-1-2-3-4-5x-5-4-3-2-112345y54321-1-2-3-4-5A)x-5-4-3-2-112345y54321-1-2-3-4-5ABx-5-4-3-2-112345y54321-1-2-3-4-5ABB)x-5-4-3-2-112345y54321-1-2-3-4-5ABx-5-4-3-2-112345y54321-1-2-3-4-5ABC)x-5-4-3-2-112345y54321-1-2-3-4-5ABx-5-4-3-2-112345y54321-1-2-3-4-5ABD)x-5-4-3-2-112345y54321-1-2-3-4-5ABx-5-4-3-2-112345y54321-1-2-3-4-5ABPage28

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Listtheinterceptsofthegraph.Tellwhetherthegraphissymmetricwithrespecttothex-axis,y-axis,origin,ornoneofthese.3)x-10-5510y105-5-10x-10-5510y105-5-10A) intercepts:(-1,0)and(1,0)symmetricwithrespecttooriginB) intercepts:(0,-1)and(0,1)symmetricwithrespecttoy-axisC) intercepts:(-1,0)and(1,0)symmetricwithrespecttox-axis,y-axis,andoriginD) intercepts:(0,-1)and(0,1)symmetricwithrespecttox-axis,y-axis,andorigin4)x-10-5510y105-5-10x-10-5510y105-5-10A) intercepts:(2,0)and(-2,0)symmetricwithrespecttox-axis,y-axis,andoriginB) intercepts:(2,0)and(-2,0symmetricwithrespecttoy-axisC) intercepts:(0,2)and(0,-2)symmetricwithrespecttooriginD) intercepts:(0,2)and(0,-2)symmetricwithrespecttox-axis,y-axis,andoriginPage29

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5)x-10-5510y105-5-10x-10-5510y105-5-10A) intercept:(0,7)symmetricwithrespecttox-axisB) intercept:(0,7)nosymmetryC) intercept:(7,0)symmetricwithrespecttoy-axisD) intercept:(7,0)nosymmetry6)x-10-5510y105-5-10x-10-5510y105-5-10A) intercept:(0,5)symmetricwithrespecttoy-axisB) intercept:(5,0)symmetricwithrespecttox-axisC) intercept:(5,0)symmetricwithrespecttoy-axisD) intercept:(0,5)symmetricwithrespecttooriginPage30

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