· 2020-02-06 · Title: M1_mod8_SEh_52016f.pdf

The Mathematics Vision Project Scott Hendrickson, Joleigh Honey, Barbara Kuehl, Travis Lemon, Janet Sutorius

© 2016 Mathematics Vision Project Original work © 2013 in partnership with the Utah State Off ice of Education

This work is licensed under the Creative Commons Attribution CC BY 4.0

MODULE 8

Connecting Algebra & Geometry

SECONDARY

MATH ONE

An Integrated Approach

SECONDARY MATH 1 // MODULE 8

CONNECTING ALGEBRA & GEOMETRY

Mathematics Vision Project Licensed under the Creative Commons Attribution CC BY 4.0 mathematicsvisionproject.org

MODULE 8 - TABLE OF CONTENTS

CONNECTING ALGEBRA AND GEOMETRY

8.1 Go the Distance – A Develop Understanding Task

Using coordinates to find distances and determine the perimeter of geometric shapes (G.GPE.7)

READY, SET, GO Homework: Connecting Algebra and Geometry 8.1

8.2 Slippery Slopes – A Solidify Understanding Task

Proving slope criteria for parallel and perpendicular lines (G.GPE.5)


8.3 Prove It! – A Practice Understanding Task

Using coordinates to algebraically prove geometric theorems (G.GPE.4)


8.4 Training Day – A Solidify Understanding Task

Writing the equation f(t) = m(t) + k by comparing parallel lines and finding k (F.BF.3, F.BF.1, F.IF.9)


8.5 Training Day Part II – A Practice Understanding Task

Determining the transformation from one function to another (F.BF.3, F.BF.1, F.IF.9)


8.6 Shifting Functions – A Practice Understanding Task

Translating linear and exponential functions using multiple representations (F.BF.3, F.BF.1, F.IF.9) READY, SET, GO Homework: Connecting Algebra and Geometry 8.6

SECONDARY MATH I // MODULE 8

CONNECTING ALGEBRA & GEOMETRY – 8.1


8.1 Go the Distance

A Develop Understanding Task

TheperformancesofthePodunkHighSchooldrillteamareverypopularduringhalf-timeattheschool’sfootballandbasketballgames.WhenthePodunkHighSchooldrillteamchoreographsthedancemovesthattheywilldoonthefootballfield,theylayouttheirpositionsonagridliketheonebelow:

Inoneoftheirdances,theyplantomakepatternsholdinglong,wideribbonsthatwillspanfromonedancerinthemiddletosixotherdancers.Onthegrid,theirpatternlookslikethis:

Thequestionthedancershaveishowlongtomaketheribbons.Gabriela(G)isstandinginthecenterandsomedancersthinkthattheribbonfromGabriela(G)toCourtney(C)willbeshorterthantheonefromGabriela(G)toBrittney(B).

1. Howlongdoeseachribbonneedtobe?

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2. Explainhowyoufoundthelengthofeachribbon.

Whentheyhavefinishedwiththeribbonsinthisposition,theyareconsideringusingthemtoformanewpatternlikethis:

3. WilltheribbonstheyusedinthepreviouspatternbelongenoughtogobetweenBritney(B)andCourtney(C)inthenewpattern?Explainyouranswer.

Gabrielanoticesthatthecalculationssheismakingforthelengthoftheribbonsremindsherofmathclass.Shesaystothegroup,“Hey,Iwonderifthereisaprocessthatwecoulduselikewhatwehavebeendoingtofindthedistancebetweenanytwopointsonthegrid.”Shedecidestothinkaboutitlikethis:

2




(x2,y2)

(x1,y1)

B

A

“I’mgoingtostartwithtwopointsanddrawthelinebetweenthemthatrepresentsthedistancethatI’mlookingfor.Sincethesetwopointscouldbeanywhere,InamedthemA(x1,y1)andB(x2,y2).Hmmmmm....whenIfiguredthelengthoftheribbons,whatdidIdonext?”

4. Thinkbackontheprocessyouusedtofindthelengthoftheribbonandwritedownyourstepshere,intermsof(x1,y1)and(x2,y2).

5. Usetheprocessyoucameupwithin#4tofindthedistancebetweentwopointslocatedfarenoughawayfromeachotherthatusingyourformulafrom#4ismoreefficientthangraphingandcounting.Forexamplefindthedistancebetween(-11,25)and(23,-16)

6. Useyourprocesstofindtheperimeterofthehexagonpatternshownin#3.

3


CONNECTING ALGEBRA & GEOMETRY - 8.1

Mathematics Vision Project

Licensed under the Creative Commons Attribution CC BY 4.0

mathematicsvisionproject.org

8.1

READY Topic:FindingthedistancebetweentwopointsUsethenumberlinetofindthedistancebetweenthegivenpoints.(ThenotationABmeansthedistancebetweenthepointsAandB.)

1.AE 2.CF 3.GB 4.CA 5.BF 6.EG

7.Describeawaytofindthedistancebetweentwopointsonanumberlinewithoutcountingthespaces.

8. a.FindAB. b.FindBC. c.FindAC.9.WhyisiteasiertofindthedistancebetweenpointAandpointBandpointBandpointCthanitistofindthedistancebetweenpointAandpointC?

10.ExplainhowtofindthedistancebetweenpointAandpointC.

–4 –2 2 40

A B C D E F G

READY, SET, GO! Name PeriodDate

CB

A

4






8.1

SET Topic:Slopetrianglesandthedistanceformula

TriangleABCisaslopetriangleforthelinesegmentABwhereBCistheriseandACistherun.NoticethatthelengthofsegmentBChasacorrespondinglengthonthey-axisandthelengthofAChasacorrespondinglengthonthex-axis.Theslopeformulaiswrittenas! = !!!!!

!!!!!wheremistheslope.

11.a.Whatdoesthevalue !! − !! tellyou?b.Whatdoesthevalue !! − !! tellyou?InthepreviousunityoufoundthelengthofaslantedlinesegmentbydrawingtheslopetriangleandthenusingthePythagoreantheoremonthetwosidesofthetriangle.Inthisexercise,trytodevelopamoreefficientmethodofcalculatingthelengthofalinesegmentbyusingthemeaningof !! − !! and!! − !! combinedwiththePythagoreantheorem.12.FindAB. 13.FindAB.14.FindAB. 15.FindAB.

10

8

6

4

2

5

x2x1

y1

y2 B

A C

5






8.1

GO Topic:RectangularcoordinatesUsethegiveninformationtofillinthemissingcoordinates.Thenfindthelengthoftheindicatedlinesegment.16.a)FindHB.b)FindBD.17.a)FindDBb)FindCF

E ( , -4)

K ( , )

C ( , )G ( , ) A (0 , 0)

B ( , 6)H ( , )

F (-10, ) D (10 , )

6




8.2 Slippery Slopes

A Solidify Understanding Task

Whileworkingon“IsItRight?”inthepreviousmoduleyoulookedatseveralexamplesthatleadto

theconclusionthattheslopesofperpendicularlinesarenegativereciprocals.Yourworkhereisto

formalizethisworkintoaproof.Let’sstartbythinkingabouttwoperpendicularlinesthatintersect

attheorigin,likethese:

1. Startbydrawingarighttrianglewiththesegment!" asthehypotenuse.Theseareoftencalledslopetriangles.Basedontheslopetrianglethatyouhavedrawn,whatistheslopeof

!"?

2. Now,rotatetheslopetriangle90°abouttheorigin.Whatarethecoordinatesoftheimage

ofpointA?

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7




3. Usingthisnewpoint,A’,drawaslopetrianglewithhypotenuse!"′ .Basedontheslopetriangle,whatistheslopeoftheline!"′?

4. Whatistherelationshipbetweenthesetwoslopes?Howdoyouknow?

5. Istherelationshipchangedifthetwolinesaretranslatedsothattheintersectionisat

(-5,7)?

Howdoyouknow?

Toproveatheorem,weneedtodemonstratethatthepropertyholdsforanypairofperpendicular

lines,notjustafewspecificexamples.Itisoftendonebydrawingaverysimilarpicturetothe

exampleswehavetried,butusingvariablesinsteadofnumbers.Usingvariablesrepresentsthe

ideathatitdoesn’tmatterwhichnumbersweuse,therelationshipstaysthesame.Let’strythat

strategywiththetheoremaboutperpendicularlineshavingslopesthatarenegativerecipricals.

8




• Lineslandmareconstructedtobeperpendicular.

• StartbylabelingapointPonthelinel.

• LabelthecoordinatesofP.

• DrawtheslopetrianglefrompointP.

• Labelthelengthsofthesidesoftheslopetriangleusingvariableslikeaandbforthe

runandtherise.

6. Whatistheslopeoflinel?

RotatepointP90°abouttheorigin,labelitP’andmarkitonlinem.Whatarethe

coordinatesofP’?

7. DrawtheslopetrianglefrompointP’.Whatarethelengthsofthesidesoftheslope

triangle?Howdoyouknow?

8. Whatistheslopeoflinem?

9. Whatistherelationshipbetweentheslopesoflinelandlinem?Howdoyouknow?

10. Istherelationshipbetweentheslopeschangediftheintersectionbetweenlinelandlinem

istranslatedtoanotherlocation?Howdoyouknow?

11. Istherelationshipbetweentheslopeschangediflineslandmarerotated?

9




12. Howdothesestepsdemonstratethattheslopesofperpendicularlinesarenegative

reciprocalsforanypairofperpendicularlines?

Thinknowaboutparallellinesliketheonesbelow.

13.DrawtheslopetrianglefrompointAtotheorigin.Whatistheslopeof!"?

14.Whattransformation(s)mapstheslopetrianglewithhypotenuse!"ontotheotherlinem?

15.Whatmustbetrueabouttheslopeoflinel?Why?

m

l

10




Nowyou’regoingtotrytousethisexampletodevelopaproof,likeyoudidwiththeperpendicular

lines.Herearetwolinesthathavebeenconstructedtobeparallel.

16.Showhowyouknowthatthesetwoparallellineshavethesameslopeandexplainwhythis

provesthatallparallellineshavethesameslope.

11






8.2

READY Topic:Usingtranslationstographlines

Theequationofthelineinthegraphis! = !.1.a)Onthesamegridgraphaparallellinethatis3unitsaboveit.

b)Writetheequationforthenewlineinslope-interceptform.

c)Writethey-interceptofthenewlineasanorderedpair.

d)Writethex-interceptofthenewlineasanorderedpair.

e)Writetheequationofthenewlineinpoint-slopeformusingthey-intercept.

f)Writetheequationofthenewlineinpoint-slopeformusingthex-intercept.g)Explaininwhatwaytheequationsarethesameandinwhatwaytheyaredifferent.

Thegraphattherightshowstheline! = −!".2.a)Onthesamegrid,graphaparallellinethatis4unitsbelowit.

b)Writetheequationofthenewlineinslope-interceptform.



e)Writetheequationofthenewlineinpoint-slopeformusing

they-intercept.



12






8.2

Thegraphattherightshowstheline! = !! !.

3.a)Onthesamegrid,graphaparallellinethatis2unitsbelowit.

b)Writetheequationofthenewlineinslope-interceptform.



e)Writetheequationofthenewlineinpoint-slopeformusingthey-intercept.


SET Topic:Verifyingandprovinggeometricrelationships

Thequadrilateralattherightiscalledakite.Completethemathematicalstatementsaboutthekiteusingthegivensymbols.Proveeachstatementalgebraically.(Asymbolmaybeusedmorethanonce.)

≅ ⊥ ∥ < > =

Proof

4.!"__________!" ______________________________________________________________________________

5.!"__________!"

6.!"__________!"

13






8.2

7.∆!"#______ ∆!"#

8.!!__________!"

9.!"__________!"

10.!"__________!"

GO

Topic:Writingequationsoflines

Usethegiveninformationtowritetheequationofthelineinstandardform. !" + !" = ! 11.!"#$%: − !

! !"#$% !",!

12.! !!,−! , ! !,!

13.! − !"#$%&$'#: − !; ! − !"#$%&$'#: − !

14.!"" ! !"#$%& !"# −! . ! !" !"# !"#$%&.

15.!"#$%: !! ; ! − !"#$%&$'#:! 16.! −!",!" , ! !",!"

14




8.3 Prove It!

A Practice Understanding Task

Inthistaskyouneedtouseallthethingsyouknowaboutquadrilaterals,distance,andslopetoprovethattheshapesareparallelograms,rectangles,rhombi,orsquares.Besystematicandbesurethatyougivealltheevidencenecessarytoverifyyourclaim.

1.

a.IsABCDaparallelogram?Explainhowyouknow.

b.IsEFGHaparallelogram?Explainhowyouknow.

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15




2.

a.IsABCDarectangle?Explainhowyouknow.

b.IsEFGHarectangle?Explainhowyouknow.

16




3.

a.IsABCDarhombus?Explainhowyouknow.

b.IsEFGHarhombus?Explainhowyouknow.

17




4.

a.IsABCDasquare?Explainhowyouknow.

18






8.3

READY Topic:Interpretingtablesofvalueasorderedpairs.

Findthevalueof! ! forthegivendomain.Write!and! ! asanorderedpair.1.! ! = 3! − 2 2.! ! = !! 3.! ! = 5!

! ! ! !, ! !

-2

-1

0

1

2

! ! ! !, ! !

-2

-1

0

1

2

! ! ! !, ! !

-2

-1

0

1

2

SET Topic:Identifyingspecificquadrilaterals

4.a)Isthefigureattherightarectangle?Justifyyouranswer.b)Isthefigureattherightarhombus?Justifyyouranswer.c)Isthefigureattherightasquare?Justifyyouranswer.

GO

Topic:Calculatingperimetersofgeometricshapes


19






8.3

Findtheperimeterofeachfigurebelow.Roundanswerstothenearesthundredth.5.

6.

7.

8.

9.

10.

20


CONNECTING ALGEBRA & GEOMETRY CONNECTING ALGEBRA & GEOMETRY



8.4 Training Day A Develop Understanding

Task

FernandoandMariaharetrainingforsixweekstoruninamarathon.Totrain,theyrunlapsaroundthetrackatEastlandHighSchool.Sincetheirschedulesdonotallowthemtoruntogetherduringtheweek,theyeachkeeparecordofthetotalnumberoflapstheyrunthroughouttheweekandthenalwaystraintogetheronSaturdaymorning.ThefollowingarerepresentationsofhoweachpersonkepttrackofthetotalnumberoflapsthattheyranthroughouttheweekplusthenumberoflapstheyranonSaturday.

Fernando’sdata:

Time(inminutesonSaturday)

0 10 20 30 40 50

Distance(inlaps)

60 66 72 78 84 90

Mariah’sdata:


cc b

y ht

tps:

//flic

.kr/

p/qq

dfiN

/

Distance(inlaps)

21


CONNECTING ALGEBRA & GEOMETRY CONNECTING ALGEBRA & GEOMETRY



1. Whatobservationscanbemadeaboutthesimilaritiesanddifferencesbetweenthetwo

trainers?

2. Writetheequation,m(t),thatmodelsMariah’sdistance.

3. FernandoandMariahbothsaidtheyranthesamerateduringtheweekwhentheyweretrainingseparately.ExplaininwordshowFernando’sequationissimilartoMariah’s.Usethesentenceframe:Therateofbothrunnersisthesamethroughouttheweek,however,

Fernando______________________________________________________.

4. Inmathematics,sometimesonefunctioncanbeusedtobuildanother.WriteMariah’sequation,m(t),bystartingwithFernando’sequation,f(t).

f(t)=

5. Usethemathematicalrepresentationsgiveninthistask(tableandgraph)tomodeltheequationyouwrotefornumber4.Writeinwordshowyouwouldexplainthisnewfunctiontoyourclass.

22






8.4

READY Topic:Verticaltransformationsongraphs

1.Usethegraphbelowtodrawanewgraphthatistranslatedup3units.

2.Usethegraphbelowtodrawanewgraphthatistranslateddown1unit.

3.Usethegraphbelowtodrawanewgraphthatistranslateddown4units.

4.Usethegraphbelowtodrawanewgraphthatistranslateddown3units.


23






8.4

SET Topic:Graphingtransformationsandwritingtheequationofthenewgraph

Youhavebeengiventheequationsof! ! andthetransformation! ! = ! ! + !.Graphboth! ! and! ! .Thenwritethelinearequationfor! ! inthespaceprovided.

5.! ! = 2! − 4; ! ! = ! ! + 3 6.! ! = 0.5!;! ! = ! ! − 3

!(!) = ____________________________

!(!) = ____________________________

Basedonthegivengraph,writetheequationof! ! intheformof! ! = ! ! + !.Thensimplifytheequationof! ! intoslope-interceptform.Theequationsof! ! isgiven.7.!( ! ) = ¼ ! – 3 8.! ! = −2! + 5

a.! ! =__________________________________Translationformb.! ! =__________________________________Slope-interceptform

a.! ! =__________________________________Translationformb.! ! =__________________________________Slope-interceptform

24






8.4

GO

Topic:Convertingunitsandmakingdecisionsbasedondata9.FernandoandMariaharetrainingforahalfmarathon.Thechartbelowdescribestheirworkoutsfortheweekjustbeforethehalfmarathon.Ahalfmarathonisequalto13.1miles.Iffourlapsmakeuponemile,doyouthinkMariahandFernandoarepreparedfortheevent?

Describehowyouthinkeachpersonwillperformintherace.Includewhoyouthinkwillfinishfirstandpredictwhatyouthinkeachperson’sfinishtimewillbe.Usethedatatoinformyourconclusionsandtojustifyyouranswers.

25


CONNECTING ALGEBRA & GEOMETRY—8.5


8.5 Training Day Part II A Solidify Understanding Task

FernandoandMariahcontinuedtraininginpreparationforthehalfmarathon.Forthe

remainingweeksoftraining,theyeachseparatelykepttrackofthedistancetheyranduring

theweek.SincetheyrantogetheratthesamerateonSaturdays,theytookturnskeepingtrack

ofthedistancetheyranandthetimeittook.Sotheywouldbothkeeptrackoftheirown

information,theotherpersonwouldusethedatatodeterminetheirowntotaldistanceforthe

week.

1. Week2:Mariahhadcompleted15morelapsthanFernandobeforetheytrainedonSaturday.

a. CompletethetableforMariah.

Time(inminutes

onSaturday)

0 10 20 30 40 50 60

Fernando:Distance

(inlaps)

50 56 62 68 74 80 86

Mariah:

Distance(inlaps)

b. WritetheequationforMariahasatransformationofFernando.EquationforMariah:m(t)=f(t)_________

2. Week3:OnSaturdaymorningbeforetheystartedrunning,FernandosawMariah’stable

andstated,“Myequationthisweekwillbef(t)=m(t)+30.”a. WhatdoesFernando’sstatementmean?

b. BasedonFernando’stranslatedfunction,completethetable.

Time(inminutes

onSaturday)

0 20 40 60 70

Fernando:Distance

(inlaps)

Mariah:

Distance(inlaps)

45 57 69 81 87

©w

ww

.flic

kr.c

om/p

hoto

s/ab

lem

an/

26




c. Writetheequationforbothrunnersinslope-interceptform:

d. WritetheequationforMariah,transformedfromFernando.

e. Whatrelationshipdoyounoticebetweenyouranswerstopartscandd?

3. Week4:Themarathonisonlyacoupleofweeksaway!

a. UseMariah’sgraphtosketchf(t).f(t)=m(t)–10


b. Writetheequationsforbothrunnersinslope-interceptform.

c. Whatdoyounoticeaboutthetwographs?Wouldthisalwaysbetrueifonepersonran

“k”lapsmoreorlesseachweek?

Distance

27




4. Week5:Thisisthelastweekoftrainingtogether.NextSaturdayisthebigday.Whentheyarrivedtotrain,theynoticedtheyhadbothrun60lapsduringtheweek.

a. WritetheequationforMariahonSaturdaygiventhattheyrunatthesamerateastheweekbefore.

b. WriteFernando’sequationasatransformationofMariah’sequation.

5. Whatconjecturescanyoumakeaboutthegeneralstatement:“g(x)=f(x)+k”whenitcomestolinearfunctions?

28






8.5

READY Topic:Describingspread.

1.Describethespreadinthehistogrambelow.

2.Describethespreadinthelineplotbelow.3.Describethespreadintheboxandwhiskerplot.


https://commons.wikimedia.org/wiki/File:Black_cherry_tree

29






8.5

SET Topic:Writingfunctionsintranslationform.

Youaregiveninformationabout! ! and! ! .Rewrite! ! intranslationform:! ! = ! ! + !

4.! ! = 7! + 13! ! = 7! − 5

!(!) = ____________________

Translationform

5.! ! = 22! − 12! ! = 22! + 213

!(!) = ____________________ Translationform

6.! ! = −15! + 305! ! = −15! − 11

!(!) = ____________________ Translationform

7.!(!) = ____________________ Translationform

x f(x) g(x)3 11 26

10 46 61

25 121 136

40 196 211


x f(x) g(x)-4 5 -42

-1 -1 -48

5 -13 -60

20 -43 -90


x f(x) g(x)-10 4 -15.5

-3 7.5 -12

22 20 0.5

41 29.5 10

GO

Topic:Verticalandhorizontaltranslations.10.Usethegraphof! ! = !"todothefollowing:a.Sketchthegraphof! ! = !" − !onthesamegrid.b.Sketchthegraphof! ! = ! ! − ! c.Describehow! ! ,! ! ,!"# ! ! aredifferentandhowtheyarethesame.d.Explaininwhatwaytheparenthesesaffectthegraph.Whydoyouthinkthisisso?

f (x)

30




8.6 Shifting Functions

A Practice Understanding Task

PartI:Transformationofanexponentialfunction.ThetablebelowrepresentsthepropertyvalueofRebekah’shouseoveraperiodoffouryears.Rebekah’sHome

Rebekahsaysthefunction! ! = 150,000 1.06 !representsthevalueofherhome.

1. Explainhowthisfunctioniscorrectbyusingthetabletoshowtheinitialvalueandthecommonratiobetweenterms.

JeremylivesclosetoRebekahandsaysthathishouseisalwaysworth$20,000morethanRebekah’shouse.Jeremycreatedthefollowingtableofvaluestorepresentthepropertyvalueofhishome.Jeremy’sHome

WhenRebekahandJeremytriedtowriteanexponentialfunctiontorepresentJeremy’spropertyvalue,theydiscoveredtherewasnotacommonratiobetweenalloftheterms.

2. UseyourknowledgeoftransformationstowritethefunctionthatcouldbeusedtodeterminethepropertyvalueofJeremy’shouse.

Time(years)

PropertyValue

CommonRatio

0 150,000 1 159,0002 168,5403 178,6524 189,372

Time(years)

PropertyValue

RelationshiptoRebekah’stable

0 170,000 1 179,0002 188,5403 198,6524 209,372

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31




Part2:Shiftyfunctions.Giventhefunctiong(x)andinformationaboutf(x),

• writethefunctionforf(x),• graphbothfunctionsonthesetofaxes,and• showatableofvaluesthatcomparesf(x)andg(x).

3. !" ! ! = 3 2 ! !"# ! ! = ! ! − 5, !ℎ!" ! ! = ________________________________

x f(x) g(x)

4. !" ! ! = 4 . 5 ! !"# ! ! = ! ! + 3, !ℎ!" ! ! = ________________________________

x f(x) g(x)

5. !" ! ! = 4! + 3 !"# ! ! = ! ! + 7, !ℎ!" ! ! = ________________________________

x f(x) g(x)

32




6. !" ! ! = 2! + 1 !"# ! ! = ! ! − 4, !ℎ!" ! ! = ________________________________

x f(x) g(x)

7. !" ! ! = −! !"# ! ! = ! ! + 3, !ℎ!" ! ! = ________________________________

x f(x) g(x)

PartIII:Communicateyourunderstanding.8. Iff(x)=g(x)+k,describetherelationshipbetweenf(x)andg(x).Supportyouranswers

withtablesandgraphs.

33






8.6

READY Topic:Findingpercentages

Mrs.Gonzaleznoticedthathernewchorusclasshadalotmoregirlsthanboysinit.Therewere32girlsand17boys.(Roundanswerstothenearest%.)1.Whatpercentoftheclassaregirls?2.Whatpercentareboys?3.68%ofthegirlsweresopranos.a.Howmanygirlssangsoprano?b.Whatpercentoftheentirechorussangsoprano?4.Only30%oftheboyscouldsingbass.a.Howmanyboyswereinthebasssection?b.Whatpercentoftheentirechorussangbass?5.Comparethenumberofgirlswhosangaltotothenumberofboyswhosangtenor.Whichmusicalsectionislarger? Justifyyouranswer.

SET Topic:Graphingexponentialequations.

6.Thinkaboutthegraphsof! = 2! and! = 2! − 4.a.Predictwhatyouthinkisthesameandwhatisdifferent.b.Useyourcalculatortographbothequationsonthesamegrid.Explainwhatstayedthesameandwhatchangedwhenyousubtracted4.Identifyinwhatwayitchanged.(Ifyoudon’thaveagraphingcalculator,thiscaneasilybedonebyhand.)


-10

-10

10

10

34






8.6

7.Thinkaboutthegraphsof! = 2! and! = 2 !!! .a.Predictwhatyouthinkisthesameandwhatisdifferent.b.Useyourcalculatortographbothequationsonthe

samegrid.Explainwhatstayedthesameandwhatchanged.Identifyinwhatwayitchanged.

GO

Topic:VerticaltranslationsoflinearequationsThegraphof! ! andthetranslationformequationof! ! aregiven.Graph! ! onthesamegridas! ! andwritetheslope-interceptequationof! ! and! ! .8.! ! = ! ! − 5a.

9.! ! = ! ! + 4a.

10.! ! = ! ! − 6a.

b.! ! =_______________________

b.! ! =_______________________

b.! ! =_______________________

c.! ! =_______________________Slope-interceptform



f (x)

f (x)

f (x)

-10

-10

10

10

35

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