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# Intermediate Algebra MTH 95

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This 18 page Class Notes was uploaded by August Feeney on Monday October 19, 2015. The Class Notes belongs to MTH 95 at Portland Community College taught by Staff in Fall. Since its upload, it has received 85 views. For similar materials see /class/224653/mth-95-portland-community-college in Math at Portland Community College.

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Date Created: 10/19/15

Mr Simonds MTH 95 Domain and Range practice problems Function Domain 394 Range lt Function Domain 394 Range lt Function Domain 4 Range Page 1 of 2 Mr Simonds MTH 95 Domain and Range practice problems Function Domain 394 Range Function Domain 394 Range Function Domain 394 Range O O O O O O O O O O O O H 6 5 4 3 2 10 12 3 4 5 6 Page2of2 Mr Simonds MTH 95 compound inequalitiesabsolute value equations and inequalities Key Concepts Compound Inequalities Absolute Value Equations and Inequalities MartinGale sections and practice problems 41 33 57 odd 43 1 10 all 11 71 every other odd 44 15 47 every other odd 63 95 odd Intersections and unions Suppose ThaT A and B are Two seTs of numbers The intersection of A and B is The seT of all numbers ThaT are in 2707 A and B This seT is symbolized as A m B The union of A and B is The seT of all numbers ThaT are in e rerA andor B This seT is symbolized as A u B ExamQIeI Suppose ThaT A is The seT L 23 4 5 6 and B is The seT 1151911 a WhaT areAu Band Am B Aug illll3J IJ39rJL7 ll 3 9013 Elmr3 b WhaTareAu Am AuandAmW Recall A 2 is a symbol used for The empty set F The seT wiTh no elemenTs This seT is also denoTed by The symbol Au y if r ms a symbol used for The set of all J J J real numbers This seT is also denoTed using inTerval noTaTion as 700 00 Page 1 of 8 Zhbl i Mr Simonds MTH 95 compound inequalitiesabsolute value equations and inequalities Exam pie 2 Graph The seT fogi 2 U4oo and wriTe a compound inequaliTy whose soluTion seT maTches The graph 307973777575747317101 I 3 I 567391039 X l 0K 77 1 Example 3 H f U 1Jktf LL14 0 Graph The soluTion seT To The compound inequaliTy x26 or xlt0 STaTe The soluTion seT using inTervaI noTaTion x L 0 x 1 C 00 D U 71079 78 r7 76 75 r4 73 72 71 01 Example 4 Graph The soluTion seT To The compound inequaliTy 3l1210 or 5 731214 STaTe The soluTion seT using inTervaI noTaTion l 1 P X 7h797377767574j7271012 V 32o 2 37Iy Lukas ts 3e 1 1 of 393i l h L 305 U 3 0 ii L 39 E ageEga w Mr Simonds MTH 0 Examgle 5 Graph The soluTion seT To each inequaliTy and sTaTe The soluTion seT To The compound inequaliTy using inTerval noTaTion xgt78 I 407977767574737271012345678I10 6 x351 71079737776757473727101234J673910 I ltx 4 xgt78cmdx 5 7 3910 quotI 71079777767574737271012 3 4J Y 4 5mm m mu Solutions to and inequalities The soluTion seT To an and39 inequaliTy beTween Two linear inequaliTies is aways one of Three Things The empTy seT The seT of all real numbers or an inTerval befweenTwo numbers which may or may noT include The endpoinTs For This reason and39 inequaliTies are ofTen wriTTen as befwee 39 inequaliTies For example we could wriTe x gt 3 and xlt 7 as 3 lt x lt 7 When wriTing inequaliTies where The variable is wriTTen beTween Two numbers The Two inequaliTy signs IllSf aways ope7 in 12 same t recf orz altxgtb agtxltb Examgle 6 Graph The inTerval 797 2 and Then wriTe an and39 inequaliTy and a befwee 39 inequaliTy whose soluTion seTs graph To ThaT inTerval r 710t7877767574737 710 1 3 4 5 6 7 s 910 19c lt1 Zq ahJ Ll Page 3 of 8 Mr Simonds MTH 95 compound inequalitiesabsolute value equations and inequalities Your turn work each of the following problems with one or two padners 1 Graph The soluTion seT To The compound inequaliTy x gt 7 4 and xlt 8 STaTe The soluTion seT quotlt lt i using inTervaI noTaTion x 710797873976757V7372710113456 910 ILv Jn v knl 1 39 f 2 Find and graph The soluTion seT To The compound inequaliTy 2 7 41 210 or 4 2tgt 10 STaTe The soluTion seT using inTervaI noTaTion l 397 I 3079737776757473J71012 4567896 9 7 10 qulvlo L olulVr 4quot5 H1 376 DJJ 3200 J L gt 3 3L 7 3 Find and graph The soluTion seT To The compound inequaliTy 75 S 4 7 x S 4 STaTe The soluTion l I IPA seT using inTervaI noTion Also wriTe a compound inequaIiTy using The word and ThaT has The same soluTion seT r I 409 3 J 5 5473 2 1 L11 1 3 4 5 6 39 8 10 g5 V 91x 4 gt10 q 1x 4 x 50 XS 9 KLO quot o 7 2X1 0 Z 7 773 Lg mu m U 00 4 WriTing 3 S x2 7 is bad m39kay RewriTe ThaT expression as a compound inequaliTy using The word andand discuss whaT39s bad abouT The siTuaTion lt 4 x27 W ff 3X 2 j 7 1 Page4of8 3 lt773 gt 3 7 Mr Simonds MTH 95 compound inequalitiesabsolute value equations and inequalities Absolute value equations and inequalities Suppose ThaT k is a gas ve real number The equaTion lyl k is equivalenT To The compound equaTion y k or y 7k The inequaliTy Iy I lt k is equivalenT To The compound inequaliTy 7k lt y lt k The inequaliTy lyl gt k is equivalenT To The compound inequaliTy y gt k or y lt 7k Exam pie 7 RewriTe each equaTion or inequaliTy as a compound equaTion or inequaliTy 2x125 t5lt9 DvH 2 go QxJ Iib q 39ETY c T I375x 9 7t38 4335x5 l 3 i ri 0 ug Viv t 44 10 off 9quot 09 l WA 5 7 C 3 7 5 quot 3 y 7 kL V 39 72x75lt7 S 111 4 47 l H 5 Difult ls ly 1 fg h 2lc ltIL gtltlgt G Page 5 of 8 Mr Simonds MTH 95 compound inequalitiesabsolute value equations and inequalities Exam Qle 8 Find The solu rion se r To each inequaliTy af rer firs r rewri ring The inequaliTy as a compound inequali ry I372xlt5 f adr i 0 K gt Afrnovlv A 4 Enact B Y Z 3 llt 45 Z lx 7 39r a 372x 45 2x 1 L1 K x44 v3 Wquot I 39139 9 uid m a M 2x676273 H H I l I 317 g 1 J UNI 3 3 14 um w gt 1 U L 1 Xi I L DJL4U1a lt L XHA lt 2 i 2 gt 1 L X44413 X44233 x 31 g X j Page 6 of 8 Exam Qle 9 Mr Simonds MTH 95 compound inequalitiesabsolute value equations and inequalities Suppose Tha r fx 2x1 and gx37x Find The solu rion se r To each of The following inequaliTies 72gxlt4 fx3 gx3 gm 30 5 4 26 3x 7 2 ml lt1 1509i 5 1 J Alf 517L quotJ S 3 3 7L i L 3 3 lg x275 Il hm J u ld l K IJ on a J JIJH dcldr L Lu 0 R 49 J Id 4quotquot J 5 Ckcch aleoiui 3 13 l 2 H L33quot quot 1 3 3 4 U og i 3113 Emirk9 LuLK uh ab j Mr Simonds MTH 95 compound inequalitiesabsolute value equations and inequalities Your turn work each of the following problems with one or two partners 1 lquot 5quot gt U 57 Find The soluTion seT To lxl gt 7 WriTe The soluTion seT using inTerval noTaTion Find The soluTion seT To I x I 7 10 lt 74 WriTe The soluTion seT using inTerval noTaTion Find The soluTion seT To Ix 71039 lt 74 Find The soluTion seT To 2 8 where 3 7 5t WriTe The soluTion seT using inTerval noTaTion Find The soluTion seT To f4 7 x 4 7 gx where 2x 7 7 and gx 9 Find The soluTion seT To 7339 gx 2 lt 710 where gx 2x 4 Page 8 of 8 Mr Simonds MTH 95 radical equations Key Concepts Solving simple radical equations Textbook sections and practice problems 76 739 odd Solving equations when the variable occurs in a radicand Isolate the radical expression on one side of the equal sign If there are two radicals write them on opposite sides of the equal sign Raise both sides of the equation to the If power where n is the index of the radical expressions Solve the resultant equation You musfcheck your solutions For example squaring both sides of equation can introduce false solutions 72 2 722 22 False True Examples Solve 3 27t4 Page 1 of2 Mr Simonds MTH 95 radical equations Solve 24x73 x Solve JEJ7x111 Page 2 of 2 Mr Simonds MTH 95 linear functions Key Concepts Linear Functions Textbook sections and practice 39 39 22 15 19 25 29 31 33 41 43 51 61 99 odd 23 3947 odd De nitions A linear function of x f is a function whose formula can be written in the form fxmxb When written in this form the constant slope of the function is m and the yintercept of the function is the point 0b De nitions An equation of form Ax By C where B at 0 defines y as a linear function of x If the equation is solved for y in the form y mx b then the constant slope of the function is m and the yintercept of the function is the point 0 b RacaLL y2 y1 x2 x1 The slope of the line connecting the points x1y1 and x2y2 is m Slope is frequently referred to as rise over runquot Lines with positive slope are increasim functions that is they go up when looked at from left to right Lines with negative slope are decreasing functions that is they go down when looked at from left to right Page 1 of 6 Mr Simunds MTH as 7 hnearmmmns Examgle 1 WhaT are The slope and yinTercepT of The funcTion gx 7 6x 2 Graph The funcTion and Then sTaTe wheTher This is an increasing funcTion or a decreasing funcTion Examgle 2 WhaT are The inTercest and slope of The funcTion defined by The equaTion 3x 74y 9 When graphed is The funcTion an increasing funcTion or a decreasing funcTion Page 2 of6 Mr Simonds MTH 95 linear functions Examgle 3 WhaT are The zeros of The funcTion 111 161 96 WhaT is The tinTercepT of The funcTion ExamQIe 4 Suppose ThaT g is a linear funcTion of form gt mt b wiTh g3 8 and g 2 23 Find The soluTion seT To The inequaIiTy g I Z 1 sTaTe The soluTion seT using inequaIiTy noTaTion Page 3 of 6 Mr Simonds MTH 95 linear functions Examgle 5 Suppose that f is a linear function of form fx mx I Find the formula for f given that f10 7 3 and f720 79 Is f an increasing function or a decreasing function What are the intercepts of f Example 6 Find the slope of the linear function include the unit when calcuaIm and slatm the slag Number of Tasty Cones sold in one hour Temperature degrees Fahrenheit Page 4 of 6 Mr Simonds MTH 95 linear functions Example 7 Find The slope of The linear funcTion include re unf when cacuafm and Shirm re sQe Gas Emissions Rate cchr Volume of beans consumed tbsp Example 8 Suppose ThaT is Missy39s weighT lb 1 weeks afTer39 she goes on a successful weighT oss dieT 0 Which formula makes sense 31 165 or39 31 165 Why b WhaT 39ncuo im unf is The slope of This funcTion c WhaT is The y inTer cep r of The funcTion and whaT does iT Tell us abouT Missy Page 5 of 6 Mr Simonds MTH 95 7 linear functions Example 9 Suppose ThaT gt is The percenTage of hairs on Mr Crab39s head ThaT are grey t years afTer his 40M BirThday and ThaT The formula for g is gt 7t 12 a WhaT 39ncud unI is The slope of This funcTion b WhaT is The yinTercepT of The funcTion and whaT does iT Tell us abouT Mr Crab c According To This model how old will Mr Crab be when he firsT goes ToTay grey Exam l The funcTion f is shown on The lefT Over whaT inTervaIs is f decreasing WhaT is True abouT The slope of f on each of These inTervaIs 39i39 Page 6 of 6

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