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# College Algebra MATH 1130

pellissippi state community college

GPA 3.92

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This 0 page Class Notes was uploaded by Brown Lowe on Sunday November 1, 2015. The Class Notes belongs to MATH 1130 at pellissippi state community college taught by Joaquim Heck in Fall. Since its upload, it has received 23 views. For similar materials see /class/232965/math-1130-pellissippi-state-community-college in Mathematics (M) at pellissippi state community college.

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Date Created: 11/01/15

Final Exam Review MATH1130 These problems are meanT only To be a guide and are noT acTual quesTions on The final exam TopicConcepT Homework Problems To Review 1 Radical FuncTion Find The domain SecTion 13 p42 24b Si using sTaTe wiTh inTerval noTaTion 30b 2 Solve a QuadraTic InequaliTy SecTion 34 p220 35 37 Si 39 3 Difference QuoTienT SecTion 15 p 67 73 75 Si 79 4 QuadraTic FuncTion Given equaTion SecTion 31 p185 85b find maximum or minimum value Si c 87 5 Polynomial FuncTion Given equaTion SecTion 42 p 272 19 find inTervals where increasing and 21 Si 23 decreasing 6 Piecewise Defined FuncTion SecTion 21 p 93 71b ApplicaTion EvaluaTe SecTion 42 p 274 73 Si 75 7 QuadraTic FuncTion SecTion 31 p183 7 Si p Find The verTex and The axis of 184 45 Si 47 symmeTry 8 ComposiTion of fx and gx SecTion 51 p 380 57 58 Si 63 9 WriTe The equaTion of a line ThaT is SecTion 22 p 108 31 parallel or perpendicular To a given line 35 Si 41 10 Solve a Polynomial EquaTion SecTion 32 p202 101 1 103 11 QuadraTic FuncTion SecTion 31 p 184 45 Si DeTermine The range 49 Find The range 12 Polynomial FuncTion SecTion 42 p 272 29 To DeTermine iTs end behavior 35 13 Polynomial FuncTion SecTion 42 pp 271272 Find how many Turning poinTs and Their 14 To 17 coordinaTes and idenTify increasing and decreasing inTervals MaTh 1130 Fall 2010 Final Exam Review Page 1 of 18 Solve a Polynomial EquaTion SecTion 44 p 299 109 Si 111 15 RaTional FuncTion SecTion 46 p 320 23 EquaTion of VerTical AsympToTes 25 27 27 Si 29 16 Use The equaTion of The TrajecTory of SecTion 31 p 185 87 Si a projecTile To find maximum heighT or 90 Time To hiT The ground 17 RaTional FuncTion EquaTion of SecTion 46 p 320 23 HorizonTal AsympToTe 25 27 27 Si 29 18 Find The inverse of a funcTion SecTion 52 p 397 45 Si 47 19 Solve an ExponenTiaI EquaTion SecTion 55 p 456 25 1 29 20 LogariThmic FuncTion STaTe The SecTion 54 p 433 13 Si domain using inTerval noTaTion 15 21 Condense a logariThmic expression SecTion 55 p 445 53 Si using The properTies of logs 55 22 Given a cosT funcTion and a revenue SecTion 23 p 128 91 Si funcTion find The inTerval where The 93 Also see sample producT breaks even ThaT is The problem worked ouT in profiT is equal To 0 answers ProfiT 2 Revenue CosT 23 ConTinuously Compounded ApplicaTion SecTion 56 p 459 94 Si Find The Time needed for conTinuous 95 growTh 24 Regression Analysis SecTion 21 p 94 89b Si Find a funcTion of besT fiT To daTa c SecTion 31 p 186 107 25 Find The average raTe of change of a SecTion 15 p 66 57 Si funcTion beTween Two values of The independenT variable 61 MaTh 1130 Fall 2010 Final Exam Review Page 2 of 18 Final Exam Review Problems wiTh Answers 1 p42 30 fx x 3 Find domain and express in inTerval noTaTion Can39T Take The square rooT of a negaTive number x 3 z 0 x z 3 The domain is 3 2 p220 35 Solve The quadraTic inequaliTy x2 x 6 g 0 MulTiply The enTire inequaliTy by 1 x2 x 6 z 0 Find inTerval boundary poinTs by seTTing equaTion To zero and solve x2 x 6 0 This can be facTored x3x20 The inTerval boundary poinTs are x 2 3 Three inTervals are possible for The soluTion 2 2 3 and 3 FirsT inTerval 2 TesT x 3 in original equaTion 32 3 6 6 6 gt 0 True 2 is parT of soluTion Second inTerval 2 3 TesT x 0 in original equaTion 02 O 6 6 6 gt 0 false 2 3 is noT parT of soluTion Third inTerval 3 TesT x 4 in original equaTion 42 4 6 6 6 gt 0 True 3 is parT of soluTion x z oo 2 u 3 co 3 p 67 79 Find The difference quoTienT DQ given fx 2x2 x 1 DQ mf fxh2xhZxh1 h fxh2x24hx2h2xh1 fxhfx 2x24hx2h2xh12x2x139 h h MaTh 1130 Fall 2010 Final Exam Review Page 3 of 18 3eon39i fxhfx 2x24hx2hzxh12x2x1 h h fxhfx a 4hx2h hili aei ili h h fxhfx 4hx2h2h h4x2h1 h h h fxh fx 4x2h1 h 4 p18585bdie Rxx402x Rx 2x 40x 2 b 40 xi b2u xv 402 2 xy 10 yd 2102 4000 yv 200 400 yd 200 Since x is in ihousends and y is in ihousends ihe company will maximize iis revenue when 10000 pleyens are menufeeiuned end ihe maximum revenue will be 200000 5 p 27221 fx 0025 045x2 5 Graph ihe funeiion and find iunning poinis use a window of Theneeneihnee v 7 quotW H turning points two ebsoluie mins and l a local mux They i w llquot be are found using 2quotd CALC The funeiion is an even funeiion end symmeinie eboui ihe y axis so ihe minimums heve ihe seme y value and each are on ebsoluie minimum Mam 1130 Fall 2010 Final Exam Review Page 4 M10 The Turning points are 3 7025 O 5 and 3 7025 6 p93 77 3 7025 Absolu re Min 0 5 Local Max 3 7025 Absolu re Min 3x 1 5gtltlt1 fgtlt 4 13x13 6 x 3ltgtltlt5 a f 3 33 1 10 f1 f2 4 f5 6 5 1 b The function is cons39rcm r on The inferval of 1 3 c f139 31 1 2 and f1 4 f139 z f1 no r confinuous also f3 4 and f3 6 3 3 f3 z f3 no r confinuous p 274 73 x 4gtlt2 x g 3 fgtlt 3gtlt2 3ltgtltlt4 x 54 x z 4 1 3 3SI 4 3z 27 36 63 f1 312 3 f4 4 54 64 54 10 Mafh 1130 Fall 2010 Final Exam Review Page 5 of 18 7 p 184 45 fx2x24x1 02 b4 a Find verTex xv b2a 42 2 1 yv 212 411 1 verTex is 1 1 Axis of symmeTry x 1 b 00 1 decreasing 100 increasing 8 p 380 58 fx 2 x and gx 1 2 x find f o gx g o fx and f o fx f o 9gtlt f9gtlt 2 9X f o 9gtlt f9gtlt 2 1 2 X X2 9 o fgtlt 9fgtlt 1 fgtlt2 9 fgtlt 9fgtlt 1 2 gt02 9 o fgtlt 9fgtlt 1 x 4x 4 f o fgtlt ffgtlt 2 fgtlt f o fx ffx 2 2 x f o fx ffx x 9 p 108 35 Find The equaTion of a line parallel To y 4x 16 Through The poinT 4 7 yy1mxX1 m4x14y17 Y 7 4X 4 y 7 4x 16 y 4x 9 MaTh 1130 Fall 2010 Final Exam Review Page 6 of 18 9 p 10231141 10 p 202 103 Find The equaTion of a line perpendicular To y 2x Through The poinT 2 5 yy1 mgtltgtlt1 y 5 12gtlt 2 y 5 L1 2 yzl6 2 m12 x12y15 Dgtlt 2375gtlt2 5134gtlt 5020 modeled The accumulaTed AIDS deaThs xyears afTer 1984 Through 1994 EsTimaTe The when year in which There were 90000 deaThs NoTe Tor1984gtlt 01985gtlt 11986gtlt 2 eTc Graph The equaTion in Y1 and graph Y2 90000 wiTh a suggesTed window o r Plotz Hot V152 5825 YZEQEBBB V3 V V Intersection HH1BBPPH52 Y500I l 1 375 25 134x value of x aT The inTersecTion Graph The TuncTion and The 1 line y 90000 Use 2quotd CALC 5inTersecT To find The inTersecTion NoTe The The value of x aT The inTersecTion is approximaTely 5 This would correspond To The year 1984 5 or 1989 There were 90000 AIDS deaThs in 1989 MaTh 1130 Fall 2010 Final Exam Review Page 7 of 18 11 p 134 45 Find the range of x 2x2 4x 1 The parabola is concave upso the upper limit on range is m The vertex can be found Xv b2a 42 2 1 Yv2 141 11 The y coordinate of the vertex is the lower limit of range kange is 1 m Alternately the function can be graphed to find the range P1B4 49 Find the range of x 34x 12x 3 Graph the function with a standard window and find the maximum The parabola opens downward and y is m 7 T i The maximum value ofy is approximately 2917 and the minimum value of y is already known as ea i The range of the function is m2917 or it imum 33333225 515557 12 Determine the end behaviorof p 272 29 x x4x even degree positive HDT TT p 272 30 x 5 12xz even degree negative HDT u p 272 31 x 28 odd degree negative HDT TJ p 272 32 x 4x 13x odd degree negative HDT N p 272 33 x x2 x 4 odd degree negative HDT N p 272 34 x x 4x 3x 3 even degree positive HDT TT p 272 35 x 01xs 2x 3x 4 odd degree positive HDT H Maih1130Fclii2010FlncliEgtltclm Review Page E of IE 13 Find Turning poinTs and inTervals on which The funcTion is increasing and decreasing of The following funcTions Graph The funcTion and find Turning poinTs using 2quotd CALC 3minimum or 4maximum Use Turning poinTs To define inTervals and by inspecTion of The graph wriTe increasing or decreasing p 271 14 fx 3x x3 Graph in a sTandard window There are Two Turning poinTs 1 2 and 1 2 The inTervals are l l 5quot oo1 Decreasing ggijgmm we 11 Increasing 7 1 co Decreasing p 272 15 fx x3 3gtltz 9x Window Find local maximum Find local minimum InTervals are oo 3 Increasing 3 1 Decreasing InTervals are 1 co Increasing p 272 16 fx x4 ex gtltzgtltz 8 an even funcTion wiTh a rooT of 0 M2 and 0 0 is a Turning poinT An even funcTion is symmeTric abouT The yaxis so from The graph one Turning poinT will be 2 16 and The oTher will be 2 16 The inTervals are oo 2 Decreasing 2 0 Increasing n 0 2 Decreasing 2 co Increasing l g Hinimum R 155555 MaTh 1130 Fall 2010 Final Exam Review Page 9 of 18 14 p 299 109 TX Xs 6X2 8X is The TemperaTure in F where X is hours pasT midnighT To 4 am DeTermine when The TemperaTure was O F Graph The funcTion and find The zeros using The Table or 2quotd CALC 22eros From The Table The zeros are 0 2 and 4 The Times ThaT The TemperaTure was O F were midnighT 2 AM and 4 AM AlTernaTely The equaTion could be solved algebraically XX 6XZT 8X OXXz6X8XX2X4 XO X ZOandX 4O X O 2 and 4 or midnighT 2 AM and 4 AM 15 Find The VerTicaI AsympToTes of p 320 23 fX 3 X2 5 VA39s found from solving 0 Xz 5 X2 5 X 1 5 p 320 25 fX x 1 3X 10 VA39s found from solving 0 X2 3X 10 OX5X 2 VA39s areX 5andX2 MaTh 1130 Fall 2010 Final EXam Review Page 10 of 18 p 32027 fx x2 2x1 x1 2x2 3x 5 2x 5 1 r esTr icTed values found from solving 0 2x2 3x 5 0 2x 5x 1 VA aT x 52 hole aT x 1 p 320 29 fx lt3X 1 r esTr icTed values found from solving 0 x 2x 1 VA aT x1 hole aT x 2 16 p 185 87 A baseball is hiT so ThaT iTs heighT in feeT afTer39 T seconds is sT 16T2 44 4 a How high is The baseball afTer39 one second s1 1612 441 4 s1 2 16 44 4 s1 32 feeT b Find The maximum heighT of The baseball Tvemx b2a 442 16 4432 1375 SW 1613752 441375 4 svemx 3425 feeT p185 90 A golf ball is hiT so ThaT iTs heighT h in feeT afTer39 T seconds is hT 16T2 60T a WhaT is The iniTial heighT of The ball T 0 hO 16T2 60T o The iniTial heighT of The ball is zero feeT b How high is The ball afTer39 15 seconds h15 16152 6015 h15 236 90 90 The golf ball is 90 feeT off The ground afTer39 15 seconds MaTh 1130 Fall 2010 Final Exam Review Page 11 of 18 c Find The maximum heighT of The golf ball new b2a 602 16 158 1875 hvem 1618752 601875 hvemx 5625 feeT The golf ball39s maximum heighT is 5625 feeT 17 Find The equaTion of The hor izonTal asympToTe of p320 23 p320 25 p320 27 p320 29 fgtlt L x2 5 y3 HA y 0 x2 fgtlt L x2 3x10 y A x2 HA does noT exisT 2 x fx x22x1 2x23x5 HAy05 fx 3x x 2 X 2x 1 y 3x2 HA y 3 X2 18 Find The inverse of a funcTion p 397 45 fx3x1 y3x1 x3y1 3yx1 ygtlt1 3 f391x x1 3 MaTh 1130 Fall 2010 Final Exam Review Page 12 of 18 18 p 397 47 19 p 456 25 19 p 456 29 fx 2x3 5 y 2x3 5 x 2y3 5 2y3 2 x 5 y3 x 52 y x 521 3 Solve for x 4quotquot1 32quot 4x 1 32x n4quot391 n32quot x 1 n4 2x n3 x n4 n4 2x n3 n4 2x n3 x n4 n4 x2 n3 n4 x n4 2 n3 n4 x 1710 SOIVe for x 314quot 4 60 314quot 4 60 314 64 14X 643 n14quot n643 x n14 n643 x In 643 n14 x 9095 20 S ra re The Domain in in rer39val no ra rion p 43313 fx log x 3 x 3 gt O xgt3 Domain is 3 00 Ma rh 1130 Fall 2010 Final Exam Review Page 13 of 18 20 p43315 fxlogx21 x2 1gt O x1x 1gt0 Xb 11 inTer39vals TesT poinT value of inequaliTy oo 1 x2 2213gto yes 11 x0 02121gt0no 11 X2 2213gt0 yes Domain is oo 1 U 1 cgt0 21 Condense a logar iThmic expression inTo one log using pr oper Ties of logar39iThms p 445 53 log 4 log x 7 log fx 3909 4 3909 X 3909 Xm log 4x72 x log 4x52 p 445 55 Zlog x2 1 4log x 2 12 log y 3909 x2 12 log x 24 log Wm 3909 x2 12x 24 WI2 22 Given a cosT funcTion and a revenue funcTion find The pr ofiT or The break even poinT Solve linear equaTions The cosT To produce x number of gizmos is 525x 14875 The revenue obTained from The sale of x gizmos is 875x a WhaT is The cosT funcTion b WhaT is The revenue funcTion c WhaT is The pr ofiT funcTion d How many gizmos have To be sold To break even a Cx 525x 14875 b Rx 875x C PX PX CX Px 875x 525x 14875 Px 35x 14875 d How many gizmos have To be sold To break even Px O 35x 14875 x 1487535 425 425 gizmos have To be sold To break even MaTh 1130 Fall 2010 Final Exam Review Page 14 of 18 p 128 91 The per capiTa income from 1980 To 2006 can be modeled by fx 1000x 1980 10000 where x is The year DeTermine The year when The per capiTa income was 19000 fx 19000 19000 1000x 1980 10000 9000 1000x 1980 9 x 1980 x 1989 p 128 93 During The 198039s The sale of compacT discs surpassed The sale of vinyl LP records From 1985 To 1990 The sale of compacT discs in millions can be modeled by The formula fx 516x 1985 91 whereas sales of vinyl LP records in millions can be modeled by The formula gx 319x 1985 1677 ApproximaTe The year when The sales of each were equal fgtlt 9X 516x 1985 91 319x 19851677 835x 1985 91 21677 835x 1985 1586 x 1985 1899 x 1986899 x z 1987 MaTh 1130 Fall 2010 Final Exam Review Page 15 of 18 23 p 459 94 For The given annual inTer esT r aTe r39 esTimaTe The Time A Pequot for P dollar39s To double P 750 and r 12 compounded conTinuously Round To Two decimal places A 1500 1500 750e 12 2 eo12 n2 ne12 n2 012T ne 1 139 139 lng2 012 5776 years 578 years p 459 95 AT Pequot wiTh r 9 P 500 AT 750 solve for T 24 p94 89 and inTer pr eT The r esulTs AT Pequot 750 500e 9 e009T n15 lne 39 9 n15 009T ne T n15 009 T 4505 500 invesTed aT 9 compounded conTinuously wiTh have a fuTur e value of 750 is appr oximaTely 45 years The Table lisTs The number of sTudenTs in millions aTTending US public school grades 912 for selecTed years where x 0 corresponds To 2000 x 1 To 2001 and so on xyear0357 I ysTudenTs I 135 MaTh 1130 Fall 2010 Final Exam Review Page 16 of 18 a Use regression To find a formula fx ax b so ThaT fgtlt models The daTa fx 02327 x 13552 r2 09871 b Graph fgtlt and The daTa inTerpreT The slope The slope is 02327 millions of sTudenTs per year IT is posiTive so ThaT The funcTion is increasing The sTudenT enrollmenT is increasing aT a raTe of 02327 million per year c EsTimaTe The enrollmenT in 2002 f2 f2 023272 13522 13984 The enrollmenT is 2002 is approximaTely 14 million sTudenTs 24 p186107 The Table lisTs The average number of people age 18 or older in a US household Year Household Size a Find a quadraTic funcTion ThaT models The daTa fx 000019838x2 07915x 791460 r2 09926 b EsTimaTe The average number of people age 18 or over in a household in 1975 f1975 00001983819752 079151975 791460 HiT 2quotd TBLSET 0 change IndpnT 0 Ask and hiT 2quotd TABLE and enTer 1975 for x and read Y1 Y1 is 19934 The average number of people age 18 or over in a household in 1975 is 199 MaTh 1130 Fall 2010 Final Exam Review Page 17 of 18

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