sduhsd math 1 module 5 seteachers.sduhsd.net/dpillsbury/im1/modules/sduhsd math 1 module … ·...

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©2012MathematicsVisionProject|MVPInpartnership withtheUtahStateOfficeofEducation

LicensedundertheCreativeCommonsAttribution‐NonCommercial‐ShareAlike3.0Unportedlicense

IntegratedMath1Module5

FeaturesofFunctions

AdaptedFrom

TheMathematicsVisionProject:ScottHendrickson,JoleighHoney,BarbaraKuehl,

TravisLemon,JanetSutoriuswww.mathematicsvisionproject.org

InpartnershipwiththeUtahStateOfficeofEducation

2

SDUHSDMath1CollegePrep

Module5OverviewPrerequisiteConcepts&Skills:

Solvemulti‐stepequations Graphlinearandexponentialfunctions Identifydomainandrangeofafunction Comparelinearandexponentialmodels Transitionfromarithmeticandgeometricsequencestolinearandexponentialmodels Distinguishbetweencontinuousvs.discrete Applylinearandexponentialfunctiontomodelsituations Solvelinearandexponentialequations Analyzerateofchangeforagivencontext Representlinearequationsusingslope‐intercept,standard,andpoint‐slopeform

SummaryoftheConcepts&SkillsinModule5:

Useacontexttographanddescribekeyfeaturesoffunctions Usetablesandgraphstointerpretkeyfeaturesoffunctions Interpretfunctionsusingnotation Combinefunctionsandanalyzecontextsusingfunctions Usegraphstosolveproblemsgiveninfunctionnotation Definefunction Identifywhetherornotarelationisafunctiongivenvariousrepresentations

ContentStandardsandStandardsofMathematicalPracticeCovered:

ContentStandards:F.IF.1,F.IF.2,F.IF.3,F.IF.4,F.IF.5,F.IF.7,F.BF.1B,A.REI.11,A.CED.3,A.CED.4, StandardsofMathematicalPractice:

1. Makesenseofproblems&persevereinsolvingthem.2. Attendtoprecision3. Reasonabstractly&quantitatively4. Constructviablearguments&critiquethereasoningofothers5. Modelwithmathematics6. Useappropriatetoolsstrategically7. Lookfor&makeuseofstructure8. Lookfor&expressregularityinrepeatedreasoning

Materials:

GraphingUtility

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Module5Vocabulary: Domain Range Function Functionnotation x‐andy‐intercepts Intervalnotation Linearmodel/equation/function Exponentialmodel/equation/function Continuousfunction Discretefunction Rateofchange Recursivenotation Explicitnotation

ConceptsUsedintheNextModule:

Developdefinitionsofrigid‐motiontransformations:translations,rotations,andreflections Examineslopeofperpendicularandparallellines Examinewhichrigidmotiontransformationcarryoneimageontoanothercongruentimage Writeandapplyformaldefinitionsoftherigid‐motiontransformations Findrotationalsymmetryandlinesofsymmetryinquadrilaterals Examinecharacteristicsofregularpolygonsthatemergefromrotationalsymmetryandlinesofsymmetry Makeandjustifypropertiesofquadrilateralsusingsymmetrytransformations Describeasequenceoftransformationsthatwillcarrycongruentimagesontoeachother EstablishtheASA,SAS,andSSScriteriaforcongruenttriangles Explorecompassandstraightedgeconstructions Writeproceduresforcompassandstraightedgeconstructionsandwhyitcreatesthedesiredobject(s)

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Module5–FeaturesofFunctions5.1UsingastorycontexttographanddescribekeyfeaturesoffunctionsandUsingtablesandgraphstointerpretkeyfeaturesoffunctions(F.IF.4,F.IF.5)WarmUp:GettingReadyforaPoolParty‐ADevelopUnderstandingTaskClassroomTask:FloatingDowntheRiver–ASolidifyUnderstandingTaskReady,Set,GoHomework:FeaturesofFunctions5.15.2Featuresoffunctionsusingvariousrepresentations(F.IF.4,F.IF.5)WarmUp:DanMeyer’s3Acts:WaterlineORGraphingLinearandExponentialFunctionsClassroomTask:FeaturesofFunctions–APracticeUnderstandingTaskReady,Set,GoHomework:FeaturesofFunctions5.25.3Interpretingfunctionsusingnotation(F.IF.2,F.IF.4,F.IF.5,F.IF.7,A.REI.11,A.CED.3)WarmUp:WritingDomainandRangeinIntervalNotationClassroomTask:TheWaterPark–ASolidifyUnderstandingTaskReady,Set,GoHomework:FeaturesofFunctions5.35.4Combiningfunctionsandanalyzingcontextsusingfunctions(F.BF.1b,F.IF.2,F.IF.4,F.IF.5,F.IF.7,A.REI.11,A.CED.3)WarmUp:UsingGraphicalRepresentationsofFunctionstoFindSolutionsClassroomTask:PoolingitTogether–ASolidifyUnderstandingTaskSet,GoHomework:FeaturesofFunctions5.45.5Usinggraphstosolveproblemsgiveninfunctionnotation(F.BF.1b,F.IF.2,F.IF.4,F.IF.5,F.IF.7,A.REI.11,A.CED.3)ClassroomTask:InterpretingFunctions–APracticeUnderstandingTaskReady,Set,GoHomework:FeaturesofFunctions5.55.6DefiningFunctionandIdentifyingwhetherornotarelationisafunctiongivenvariousrepresentations(F.IF.1,F.IF.3)WarmUp:ToFunctionorNottoFunction–APracticeUnderstandingTaskClassroomTask:AWaterFunction–ASolidifyUnderstandingTaskReady,Set,GoHomework:FeaturesofFunctions5.65.7Matchingfeaturesandrepresentationsofaspecificfunction(F.IF.2,F.IF.4,F.IF.5,F.IF.7,A.REI.11,A.CED.3)WarmUp:KeyFeaturesofFunctionsClassroomTask:MatchthatFunction–APracticeUnderstandingTaskReady,Set,GoHomework:FeaturesofFunctions5.7Homework:IntroducingTransformations

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© www.flickr.com/photos/jensm

ith826 5.1WarmUp

GettingReadyforaPoolParty–ADevelopUnderstandingTaskSylviahasasmallpoolfullofwaterthatneedstobeemptiedandcleaned,thenrefilledforapoolparty.Duringtheprocessofgettingthepoolready,Sylviadidallofthefollowingactivities,eachduringadifferenttimeinterval.

Removedwaterwithasinglebucket Filledthepoolwithahose(samerateasemptyingpool)

Drainedwaterwithahose(samerateasfillingpool)

Cleanedtheemptypool

Sylviaandhertwofriendsremovedwaterwiththreebuckets

Tookabreak

1. Sketchagraphshowingtheheightofthewaterlevelinthepoolovertime.Besuretoincludeallofactivities

Sylviadidtopreparethepoolfortheparty.Rememberthatonlyoneactivityhappenedatatime.Thinkcarefullyabouthoweachsectionofyourgraphwilllook,labelingwhereeachactivityoccurs.

2. WriteastoryconnectingSylvia’sprocessforemptying,cleaning,andthenfillingthepooltothegraphyouhave

created.Doyourbesttouseappropriatemathvocabulary. 3. a. Doesyourgraphrepresentafunction?Whyorwhynot?

b. Wouldallgraphscreatedforthissituationrepresentafunction?

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5.1FloatingDowntheRiverASolidifyUnderstandingTask Alonzo,Maria,andSierrawerefloatingininnertubesdownariver,enjoyingtheirday.Alonzonoticedthatsometimesthewaterlevelwashigherinsomeplacesthaninothers.Marianoticedthereweretimestheyseemedtobemovingfasterthanatothertimes.Sierralaughedandsaid“Mathiseverywhere!”Tolearnmoreabouttheriver,AlonzoandMariacollecteddatathroughoutthetrip.Alonzocreatedatableofvaluesbymeasuringthedepthofthewatereverytenminutes.

Time(inminutes)

0 10 20 30 40 50 60 70 80 90 100 110 120

Depth(infeet) 4 6 8 10 6 5 4 5 7 12 9 6.5 5

1. UsethedatacollectedbyAlonzotointerpretthekeyfeaturesofthisrelationship.MariacreatedagraphbycollectingdataonaGPSunitthattoldherthedistanceshehadtraveledoveraperiodoftime.

2. UsingthegraphcreatedbyMaria,describethekeyfeaturesofthisrelationship.

©www.flickr.com

/photos/hamiltonca

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3. Sierralookedatthedatacollectedbyhertwofriendsandmadeseveralofherownobservations.Explainwhyyoueitheragreeordisagreewitheachobservationmade.

a. Thedepthofthewaterincreasesanddecreasesthroughoutthe120minutesoffloatingdowntheriver.

Agree/Disagree Why?

b. Thedistancetraveledisalwaysincreasing.

Agree/Disagree Why?

c. Thedistancetraveledisafunctionoftime.

Agree/Disagree Why?

d. Thedistancetraveledisgreatestduringthelasttenminutesofthetripthanduringanyothertenminuteintervaloftime.

Agree/Disagree Why?

e. Thedomainofthedistancevs.timegraphisallrealnumbers.

Agree/Disagree Why?

f. They‐interceptofthedepthofwaterovertimefunctionis 0, 0 .

Agree/Disagree Why?

g. Thedistancetraveledincreasesanddecreasesovertime.

Agree/Disagree Why?

h. Thewaterlevelisafunctionoftime.

Agree/Disagree Why?

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i. Therangeofthedistancevs.timegraphisfrom 0, 15000 .

Agree/Disagree Why?

j. Thedomainofthedepthofwaterwithrespecttotimeisfrom 0, 120

Agree/Disagree Why?

k. Therangeofthedepthofwaterovertimeisfrom 4, 5 .

Agree/Disagree Why?

l. Thedistancevs.timegraphhasnomaximumvalue.

Agree/Disagree Why?

m. Thedepthofwaterreachedamaximumat30minutes.

Agree/Disagree Why?

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Name: FeaturesofFunctions 5.1Ready,Set,Go!ReadyTopic:SolvesystemsbygraphingGrapheachsystemoflinearequationsandfindwhere .1. 5 2

2 1

2. 4

1

3. 3

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SetTopic:Describingattributesofafunctionbasedonthegraphicalrepresentation.Foreachgraphgiven,matchittothecontextualdescriptionthatfitsbest.Thenlabeltheindependentanddependentaxesoneachgraphwiththepropervariables. Graphs ContextualDescriptions

4.

a. Theamountofmoneyinasavingsaccountwhereregulardepositsandsomewithdrawalsaremade.

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b. Thetemperatureoftheovenonadaythatmombakesseveralbatchesofcookies.

6.

c. Theamountofgasolineonhandatthegasstationbeforeatankertruckdeliversmore.

7.

d. Thenumberofwatermelonsavailableforsaleatthefarmer’smarketonThursday.

8.

e. Theamountofmileagerecordedontheodometerofadeliverytruckoveratimeperiod.

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Giventhepairofgraphsoneachcoordinategrid,createalistofsimilaritiesthetwographsshareandalistofdifferences.Considerattributeslike,continuous,discrete,increasing,decreasing,linear,exponential,restrictionsondomainorrange,etc.9.

Similarities:

Differences:10.

Similarities:Differences:

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GoTopic:SolvingequationsFindthevalueofxineachequation.11.10 100,000 12.3 7 5 21 13. 6 15 4 3514.5 8 37 15.3 81 16.3 12 4 2317.10 2 22 18.243 8 3 19.5 7 118

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5.2AlternateWarmUpGraphingLinearandExponentialFunctions Grapheachofthefunctions.1. 2 5 2. 4 3 3. 5 3

4. 4 2 5. 2.5 4 6. 8 3

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©www.flickr.com

/photos/intercontinentalhongkong

5.2FeaturesofFunctionsAPracticeUnderstandingTaskForeachgraph,determineiftherelationshiprepresentsafunction.Ifso,statethekeyfeaturesofthefunction(intervalswherethefunctionisincreasingordecreasing,themaximumorminimumvalueofthefunction,domainandrange,andx‐andy‐intercepts.).1. 2.

3. 4.

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5.

6. 7.

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Thefollowingrepresentsacontinuousfunctiondefinedontheintervalfrom , .

8. Determinethedomain,range,x‐ andy‐intercepts.9. Basedonthetable,identifytheminimumvalueandwhereitislocated.

0 21 32 03 24 65 126 20

Thefollowingrepresentsadiscretefunctiondefinedontheintervalfrom , .

10.Determinethedomain,range,x‐ andy‐intercepts.11.Basedonthetable,identifytheminimumvalueandwhereitislocated.

1 42 103 54 85 3

Describethekeyfeaturesforeachsituation.12.Theamountofdaylightdependentonthetimeofyear.13.Thefirstterminasequenceis12.Eachconsecutivetermisexactly ofthepreviousterm.14.Marcusboughta$900couchonasixmonths,interestfree,paymentplan.Hemakes$50paymentstotheloan

eachweek.15.Thefirstterminasequenceis36.Eachconsecutivetermis lessthanthepreviousterm.16.Anempty15gallontankisbeingfilledwithgasolineatarateof2gallonsperminute.

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Foreachequation,sketchagraphandshowkeyfeaturesofthegraph.17. 2 4,when 0

18. 3

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Name: FeaturesofFunctions 5.2Ready,Set,Go!ReadyTopic:SolvesystemsbygraphingGrapheachsystemoflinearequationsandfindwhere .1. 2 7

4 5

2. 22 8

3. 5

Topic:Creatinggraphicalrepresentationsandnamingthedomain.Sketchagraphtorepresenteachfunction,andthenstatethedomainofthefunction.4 Asequenceoftermssuchthat 5. Asequenceoftermssuchthat

0 1, 1 7 0 8, 1

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SetTopic:Describefeaturesofafunctionfromitsgraphicalrepresentation.Foreachgraphgivenprovideadescriptionofthefunctionwhichincludesthetypeoffunction(ifknown),intervalswherethegraphisdecreasing&increasing,domain/range,andminimumandmaximumvalues(iftheyexist).

6. Descriptionoffunction: 7. Descriptionoffunction: Typeoffunction: Typeoffunction: Decreasing: Decreasing: Increasing: Increasing: Domain: Domain: Range: Range: Max: Max: Min: Min:Topic:Attributesoflinearandexponentialfunctions.Determineifthestatementistrueorfalse,thenjustifywhy.8. Alllinearfunctionsareincreasing.

True/FalseWhy?9. Arithmeticsequencesareanexampleoflinearfunctions.

True/FalseWhy?10.Exponentialfunctionshaveadomainthatincludesallrealnumbers.

True/FalseWhy?11.Geometricsequenceshaveadomainthatincludesallintegers.

True/FalseWhy?12.Therangeforanexponentialfunctionincludesallrealnumbers.

True/FalseWhy?13.Alllinearrelationshipsarefunctionswithadomainandrangecontainingallrealnumbers.

True/FalseWhy?.

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GoTopic:Createequationsusingbothexplicitandrecursivenotation.Writeequationsforthegiventablesinbothrecursiveandexplicitform.14. 15. 16.

n 1 62 123 24

n0 132 53 1

n1 54 115 13

Explicit: Explicit: Explicit:Recursive: Recursive: Recursive:Topic:Determinethedomainofafunctionfromthegraphicalrepresentation.Foreachgraphdeterminethedomainofthefunction.17. 18.

Domain: Domain:

19. 20.

Domain: Domain:

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5.3WarmUpWritingDomainandRangeinIntervalNotationGiventhegraphs,identifythedomainandrangeinintervalnotation.1.

Domain:Range:

2.

Domain:Range:

3.

Domain:Range:

4.

Domain:Range:

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©www.flickr.com

/photos/ableman/ 5.3TheWaterPark

ASolidifyUnderstandingTaskAlyandDayneworkatawaterparksupervisingdifferentrides.Theyhavetodrainthewaterattheendofeachmonthfortheridetheysupervise.Eachusesapumptoremovethewaterfromthesmallpoolatthebottomoftheirride.ThegraphbelowrepresentstheamountofwaterinAly’spool, ,andDayne’spool, ,overtime.

PartI1. Listasmanyobservations,aspossible,withtheinformationgiveninthegraphabove.

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PartIIDaynefiguredoutthatthepumpheusesdrainswateratarateof1000gallonsperminuteandtakes24minutestodrain.2. WritetheequationtorepresentthedrainingofDayne’spool, .Whatdoeseachpartoftheequation

represent?3. Basedonthisnewinformation,correctlyscaletheaxesonthegraphabovequestion1.4. Whatvaluesofxmakesenseinthissituation?Useintervalnotationtowritethedomainofthesituation.5. Determinetherange,oroutputvalues,thatmakesenseinthissituation.Writetherangeinintervalnotation.6. WritetheequationusedtorepresentthedrainingofAly’spool, .Usingintervalnotation,statethedomain

andrangeforthefunction, ,aswellasthedomainandrangeofthesituation.Comparethetwodomainsbydescribingtheconstraintsmadebythesituation.

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PartIIIBasedonthegraphandcorrespondingequationsforeachpool,answerthefollowingquestions.7. Whenis ?Whatdoesthismeanintermsofthesituation?8. Find 10 .Whatdoesthismeanintermsofthesituation?9. If 2000,then .Whatdoesthismeanintermsofthesituation?10.Whenis ?Whatdoesthismeanintermsofthesituation?

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Name: FeaturesofFunctions 5.3Ready,Set,Go!ReadyTopic:Attributesoflinearandexponentialfunctions.1. Writeawell‐developedparagraphcomparingandcontrastinglinearandexponentialfunctions.Besureto

includeasmanycharacteristicsofeachfunctionaspossibleandbeclearaboutthesimilaritiesanddifferencesthesefunctionshave.

SetTopic:Identifyingattributesofafunctionfromitsgraphicalrepresentation.Basedonthegraphgivenineachproblembelow,identifythedomain,range,intervalsofincreaseanddecrease.2.

Domain:Range:Increasing:Decreasing:

3.


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4.


5.


6.


7.


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8.


9.


GoTopic:FindingequationsandrulesforfunctionsFindboththeexplicitandtherecursiveequationsforeachtableofvaluesbelow.10. 11. 12.

n 1 32 53 74 9

n2 43 84 165 32

n6 237 198 159 11

Explicit: Explicit: Explicit:Recursive: Recursive: Recursive:

13. 14. 15.

n 1 12 33 9

n3 84 45 2

n6 79 1312 19


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16. 17. 18.

n 2 404 328 16

n2 163 44 1

n17 520 1026 20


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5.4WarmUpUsingGraphicalRepresentationsofFunctionstoFindSolutionsUsethegraphofeachfunctionprovidedtofindthevaluesindicated.

1.

a. 4 b. 4 c. 4, d. 7,

2.

a. 1 b. 3 c. 4, d. 1,

3.

a. 0 b. 3 c. 1, d. 2,

4.

a. 5 b. 4 c. 4, d. 0,

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©www.flickr.com

/photos/neilt

5.4PoolingItTogether ASolidifyUnderstandingTaskAlyandDayneworkatawaterparkandhavetodrainthewaterattheendofeachmonthfortheridetheysupervise.Eachusesapumptoremovethewaterfromthesmallpoolatthebottomoftheirride.ThegraphbelowrepresentstheamountofwaterinAly’spool,

,andDayne’spool, ,overtime.Inthisscenario,theydecidedtoworktogethertodraintheirpoolsandcreatedtheequation ).Thefirstgraphbelowshows and separately.Ontheblankaxesbelow,drawthegraphof andscaletheaxesappropriately.

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Answerthefollowingquestionsabout .1. Whatdoes represent?2. Namethefeaturesof andexplainwhateachmeans(x‐andy‐intercepts,domainandrangeforthis

situationandfortheequation,maximaandminima,whetherornot isafunction,etc.)3. Writetheequationfor usingtheinterceptsfromthegraph.Comparethisequationtothesumofthe

equationscreatedfor and fromTheWaterParktask.Shouldtheybeequivalent?Whyorwhynot?4. Whatdoyounoticeabouthowthefunctions , and relatetotheirgraphs?(Hint:Thinkaboutthe

keyfeaturesofthesefunctions,suchasintercepts,slope,etc…andmaybestartwithatable).ForATwist:5. IfAlyandDayne’sbossstartedtodrainthewaterbeforetheyarrivedandwhentheygotthere,therewas

already5,000lessgallonsofwatertobedrained,howwouldthisimpacttheequation?6. Writethenewequationrepresentinghowlongitwilltakethemtodrainthetwopools.

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Name: FeaturesofFunctions 5.4Set,Go!SetTopic:Givencontextofafunctionfindsolutions.Foreachsituationeithercreateafunctionorusethegivenfunctiontofindandinterpretsolutions.1. Francollecteddataonthenumberoffeetshecouldwalkeachsecondandwrotethefollowingruletomodel

herwalkingrate 4 .

a. WhatisFranlookingforifshewrites“ 12 ”?

b. Inthissituationwhatdoes 100tellyou?

c. Howcanthefunctionrulebeusedtoindicateatimeof16secondswaswalked?

d. Howcanthefunctionrulebeusedtoindicatethatadistanceof200feetwaswalked?2. Ms.Callahanworkshardtobudgetandpredicthercostsforeachmonth.Sheiscurrentlyattemptingto

determinehowmuchhercellphonecompanywilllikelychargeherforthemonth.Sheispayingaflatfeeof$80amonthforaplanthatallowsforunlimitedcallingbutcostsheranadditionaltwentycentspertextmessage.a. Writeafunction, ,forMs.Callahan’scurrentcellplanthatwillcalculatethecostforthemonthbasedon

thenumberoftextmessagesshemakes. b. Find 20 c. Find 100 d. Find 45 e. Find 90

f. For$20shecanaddunlimitedtextingtohercurrentplan.Atwhatnumberoftextswouldthisoptionbe

lessexpensivethanhercurrentplan?

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3. Mr.Multbankhasdevelopedapopulationgrowthmodelfortherodentsinthefieldbyhishouse.Hebelievesthatstartingeachspringthepopulationcanbemodeledbasedonthenumberofweekswiththefunction

8 2 a. Find 128 b. Find 4 c. Find 10

d. Findthenumberofweeksitwilltakeforthepopulationtobeover20,000.e. Inayearwith16weeksofsummer,howmanyrodentswouldheexpectbytheendofthesummerusing

Mr.Multbank’smodel?f. Whataresomefactorsthatcouldchangetheactualresultfromyourestimate?

GoTopic:DiscreteandcontinuousForeachcontextorrepresentationdeterminewhetheritisdiscreteorcontinuousorcouldbemodeledbestinadiscreteorcontinuouswayandstatewhy.4. Susanhasasavingsplanwheresheplaces$5aweekinherpiggybank.

Discrete/ContinuousWhy?

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5. 6.

Discrete/Continuous Discrete/Continuous

Why? Why?7. Marshaltracksthenumberofhitshegetseachbaseballgameandisrecordinghistotalnumberofhitsforthe

seasoninatable.


8. Thedistanceyouhavetraveledsincethedaybegan.


9.

NumberofGumBalls

Cost

5 110 215 320 4


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©www.flickr.com

/photos/alanenglish 5.5InterpretingFunctions

APracticeUnderstandingTaskGiventhegraphof ,answerthefollowingquestions.Unlessotherwisespecified,restrictthedomainofthefunctiontowhatyouseeinthegraphbelow.Approximationsareappropriateanswers.1. Whatis 2 ?_____________________2. Forwhatvalues,ifany,does 3?___________________3. Whatisthex‐intercept?_____________________4. Whatisthedomainof ?_____________________5. Onwhatintervalsis 0?_____________________6. Onwhatintervalsis increasing?_____________________7. Onwhatintervalsis decreasing?____________________8. Forwhatvalues,ifany,is 3?_____________________Considerthelineargraphof andthenonlineargraphof toanswerquestions9‐14.Approximationsareappropriateanswers.9. Whereis ?_____________________10.Whereis ?_____________________11.Whatis 0 0 ?_____________________12.Whatis 1 1 ?_____________________13.Whichisgreater: 0 or 3 ?_____________________14.Graph: from 1, 3 ____________________

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Thefollowingtableofvaluesrepresentstwocontinuousfunctions, and .Usethetabletoanswerthefollowingquestions:

15.Whatis 3 ?16.Forwhatvalue(s)is 0?17.Forwhatvaluesis increasing?18.Onwhatintervalis 19.Whichfunctionischangingfasterintheinterval 5, 0 ?Why?

Usethefollowingrelationshipstoanswerthequestionsbelow.

2 3 2 5 4 5 120.Whichoftheaboverelationsarefunctions?Explain.21.Find: 2 _____________________ 2 _____________________ 2 _____________________22.Writetheequationfor .23.Whereis ?24.Whereis increasing?25.Whichoftheabovefunctionshasthefastestgrowthrate?

5 42 134 30 93 20 52 12 11 6 30 2 71 0 112 0 153 2 194 6 235 12 276 20 31

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Name: FeaturesofFunctions 5.5Ready,Set,Go!ReadyTopic:SolvesystemsofequationsSolveeachsystemofequationseitherbysubstitutionorelimination.Useeachmethodatleastonce.Grapheachtoshowthesolution.1. 3

1

2. 6 32

3. 4

1

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SetTopic:ConnectingcontexttographicalrepresentationsForeachgraphcreateacontext,provideindependentanddependentvariablesthatwillfitthecontextyouchoose(labeltheaxeswithyourchoices).Thencreateastorythatdescribeswhatishappeningonthegraph.4.

Descriptionofcontextandastoryforthegraph:5.

Descriptionofcontextandastoryforthegraph:

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GoTopic:Describefeaturesofafunctionfromitsgraphicalrepresentation.Foreachgraphgivenprovideadescriptionofthefunction.Besuretoconsiderthefollowing:decreasing/increasing,min/max,domain/range,etc.6.

Decreasing:Increasing:Min:Max:Domain:Range:

7. Decreasing:Increasing:Min:Max:Domain:Range:

8.


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9.


Topic:Solvingliteralequationsforaspecifiedvariable.Rewriteeachequationinslope‐interceptform( ).10.12 3 6 11. 5 3 2 12. 9 4 2Writeanexplicitfunctionforthelinearfunctionthatgoesthroughthegivenpointwiththegivenslopesimplifiedintoslope‐interceptform.13. 3 1, 2 14. 4, 2

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5.6WarmUpToFunctionorNottoFunction–APracticeUnderstandingTaskDetermineifthefollowingrelationshipsarefunctions(bystatingyesorno).Besuretojustifyyourchoice. 1. Aperson’sfirstnameversustheirstudentidnumber.

2. Aperson’sstudentidnumberversustheirfirstname.

3. Thecostofgasversustheamountofgaspumped.

4. 3,6 , 4,10 , 8,12 , 4,10

5. ThetemperatureindegreesFahrenheitinSanDiegowithrespecttothetimeofday.

6.Distance Days

6 210 46 59 8

7. Theareaofacircleasitrelatestotheradius.

8.

3 55 57 7

9. Thelengthoffenceneededwithrespecttotheamountofareatobeenclosed

10.Thesizeoftheradiusofacircledependentonthearea.

11. Studentslettergradedependentonthepercentearned.

12. 4 62 78 36 41

13.Theexplicitformulafortherecursivesituationbelow:

1 3and1 4

14. Ifx is arationalnumber,then1

Ifxisanirrationalnumber,then 0

15.Time Money14 7018 8222 8225 90

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5.6AWaterFunctionASolidifyUnderstandingTaskAndrewwalkedaroundthewaterparktakingphotosofhisfamilywithhisphone.Later,hediscoveredhisphonewasmissing.Sothatotherscouldhelphimlookforhislostphone,hedrewapicturethat‘retracedhissteps’showingwherehehadwalked.

1. IfwewantedtodetermineAndrew’slocationintheparkwithrespecttotime,wouldhislocationbeafunction

oftime?Whyorwhynot?Explain.

©www.flickr.com

/photos/battlecreekcvb

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Refertothepicturewiththearrowsabovequestion1toanswerthefollowingquestions.2. SituationA:SketchagraphofthetotaldistanceAndrewwalkedifhewalkedataconstantratetheentiretime

(labelyouraxes).

3. SituationB:SketchagraphofAndrew’sdistancefromtheentrance(hisstartingpoint)asafunctionoftime

(labelyouraxes).

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4. a. HowwouldthegraphofeachsituationchangeifAndrewstoppedattheslideforaperiodoftime?Showthechangesonthegraphsbelow.

SituationA: SituationB:

b. Wouldthischangewhetherornotthissituationisafunction?

5. Howdidyoudecideonkeyfeaturesofthegraphs?Discussthesedecisionsbelow.Includeinyourdiscussion:

intervalsofincrease,intervalsofdecrease,domain,range,maximumsandminimums.

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Name: FeaturesofFunctions 5.6Ready,Set,Go!ReadyTopic:Determinedomainandrange,andwhetherarelationisafunctionornotafunction.Determineifeachsetoforderedpairsisafunctionornotthenstatethedomainandrange.1. 7, 2 , 3, 5 , 8, 4 , 6, 5 , 2, 3 Function:Yes/No Domain: Range:2. 9, 2 , 0, 4 , 4, 0 , 5, 3 , 2, 7 , 0, 3 , 3, 1 Function:Yes/No Domain: Range:3. 1, 2 , 2, 3 , 3, 4 , 4, 5 , 5, 6 , 6, 7 , 7, 8 , 8, 9 Function:Yes/No Domain: Range:Fortherepresentationofthefunctiongivendeterminethedomainandrange.4. 5.

Domain: Domain:

Range: Range:

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SetTopic:ComparingfunctionsfromdifferentrepresentationsUsethegivenrepresentationofthefunctionstoanswerthequestions.9.

a. Wheredoes ? b. Whatis 4 4 ? c. Whatis 2 2 ? d. Onwhatintervalis ? e. Sketch onthegraphprovided.

10.Thefunctions and aredefinedinthetablebelow.Eachfunctionisasetofexactlyfiveorderedpairs.

3 1 1

1 7 5

0 3 10

2 8 2

7 3 3 a. Whatis 3 3 ? b. Whatis 1 1 ? c. Whatis 0 0 ?d. Completetheadditionalcolumnsinthetablewith inonecolumnand intheother

column.

6. 2 7 Domain: Range:

7. 3 5 Domain: Range:

8. Theelementsinthetabledefinetheentiretyofthefunction.

x1 92 983 9874 9876

Domain: Range:

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11. a. Whereis ? b. Whatis 1 1 ? c. Whatis 0 0 ? d. Createanexplicitrulefor andfor . e. Sketch onthegraph

12.

a. Wheredoes ? b. Whatis 4 4 ? c. Whatis 2 2 ? d. Onwhatintervalis ? e. Sketch onthegraphprovided.

Topic:Determinewhetherornottherelationshipisafunction.Determineiftherelationshippresentedisafunctionornotandprovideajustification.13.ThedistanceapersonisfromthegroundrelatedtotimeastheyrideaFerrisWheel.14.Theamountofdaylightduringadaythroughoutthecalendaryear.15.ThevalueofaVolkswagenBugconvertiblefromtimeoffirstpurchasein1978tonow.16.Aperson’snameandtheirphonenumber.

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17.Thestadiuminwhichafootballplayerisplayingrelatedtotheoutcomeofthegame.GoTopic:Determiningfeaturesoffunctionsandfindingsolutionsusingfunctions.18.Forthegraphgivenbelow,describetheintervalsofdecrease/increase,min/max,anddomain/range.

Decreasing: Increasing: Min: Max:Domain: Range:

19.Forthegivensituationusethefunctiontofindandinterpretsolutions.

Hopehasbeentrackingtheprogressofherfamilyastheytravelacrossthecountryduringtheirvacationandshehascreatedafunction, 78 tomodeltheprogresstheyaremaking,wheretrepresentsthenumberofdaysand representsthemilestraveled.

a. WhatwouldHopebeattemptingtofindifshewrites: 4 78 4 ?

b. Whatwould 450meaninthissituation?

c. Whatwould 3.5 meaninthissituation?

d. HowcouldHopeusethefunctiontofindthetimeitwouldtaketotravel800miles?

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Usethegivenrepresentationofthefunctionstoanswerthequestions.20. a. Wheredoes ?

b. Whatis 0 0 ? c. Onwhatinterval(s)is ? d. Whatis 8 8 ?

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5.7WarmUpKeyFeaturesofFunctionUsethegivendescriptionofseveralofthekeyfeaturesofthefunctiontosketchapossiblegraphofthefunction.1. Domainis 2, 3 .

Rangeis 3, 7 .

Thefunctionisincreasingovertheinterval 2, 0 anddecreasingafter0.

Thefunctionisnotcontinuousateverypoint.

2. Thedomainofthefunctionis 5,∞

Therangeofthefunctionis 0,∞

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Name: FeaturesofFunctions 5.7Ready,Set,GoReadyTopic:Findtheoutputorinputbasedonwhatisgiven.Foreachfunctionfindthedesiredsolutions.1. 2 5

a. 4 b. 23, c. 13 d. 33,2. 3.

a. 2 a. 1 b. 3, b. 4, c. 0 c. 2 d. Whatistheexplicitrulefor d. Whatistheexplicitrulefor

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SetTopic:Describingthekeyfeaturesoffunctionsandcreatingarepresentationofafunctiongiventhekeyfeatures.Usethegivendescriptionofseveralofthekeyfeaturesofthefunctiontosketchapossiblegraphofthefunction.4. Thefunctionhasaminimumat 5.

Thefunctionhasamaximumat8.

Thefunctionhastwointervalsonwhichitisdecreasingandoneintervalonwhichitisincreasing.

ThedomainofthefunctionscontainsallRealnumbersfrom1to9.

5. Thisfunctionisnotcontinuousanywhere.

Thefunctioncontainsonlysevenelementsinitsdomain.

Thevaluesofthedomainarebetween 9and2.

Thevaluesoftherangearefrom 1and1.6. Thefunctionhasthreeintervalsonwhichitsslopeiszero.

Thefunctionhasamaximumandaminimum.

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GoTopic:FeaturesoffunctionsDescribethefollowingfeaturesofthefunction:Domain,range,whetherornotthefunctioniscontinuous,intervalswherethefunctionisincreasinganddecreasing,minimumandmaximumvalues.7. 8.

Domain: Domain:Range: Range:Continuous:Yes/No Continuous:Yes/NoIncreasing: Increasing:Decreasing: Decreasing:Minimum: Minimum:Maximum: Maximum:

9. 10.

Domain: Domain:Range: Range:Continuous:Yes/No Continuous:Yes/NoIncreasing: Increasing:Decreasing: Decreasing:Minimum: Minimum:Maximum: Maximum:

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11. 0 2, 1 ⋅ 3 12. 9 4 Domain: Domain:Range: Range:Continuous:Yes/No Continuous:Yes/NoIncreasing: Increasing:Decreasing: Decreasing:Minimum: Minimum:Maximum: Maximum:

13. | |

Domain:Range:Continuous:Yes/NoIncreasing:Decreasing:Minimum:Maximum:

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Module5TestDayHomework:IntroducingTransformationsAdaptedfromCPMGeometryUnit5CG14Inyourownwords,describehowyouwouldmovethefigureonthelefttocoincidewiththeoneontheright.Imagineyouarewritingasetofdirectionsforafriendtofollowthatwillusetheoriginalfiguretogetthefigureontheright.Beprecise!1.

2.

3.

4.

5.

6.

sduhsd math 1 module 5 seteachers.sduhsd.net/dpillsbury/im1/modules/sduhsd math 1 module … ·...

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