2.3 Linear, Exponential or Neither? d A - Utah Education … MATH 1 // MODULE 2 LINEAR & EXPONENTIAL FUNCTIONS – 2.3 Mathematics Vision Project Licensed under the Creative Commons

SECONDARY MATH 1 // MODULE 2

LINEAR & EXPONENTIAL FUNCTIONS – 2.3

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

2.3 Linear, Exponential or Neither?

A Practice Understanding Task

Foreachrepresentationofafunction,decideifthefunctionislinear,exponential,orneither.Giveatleast2reasonsforyouranswer.

1.

Linear Exponential Neither

Why?

2. TennisTournament

Rounds 1 2 3 4 5Number

ofPlayersleft

64 32 16 8 4

Thereare4playersremainingafter5rounds


Why?

CCBYJohn

Sho

rtland

https://flic.kr/p/a8u

zeA

13




3.! = 4!


Why?

4.Thisfunctionisdecreasingataconstantrate.


Why?

5. Linear Exponential Neither

Why?

14




6.Aperson'sheightasafunctionofaperson'sage(fromage0to100)


Why?

7.−3! = 4! + 7


Why?

8.x y-2 230 52 -134 -316 -49


Why?

15




9.HeightinInches ShoeSize

62 674 1370 967 1153 458 7


Why?

10.ThenumberofcellphoneusersinCentervilleasa

functionofyears,ifthenumberofusersis

increasingby75%eachyear.


Why?

11. Linear Exponential Neither

Why?

16




12.Thetimeittakesyoutogettoworkasafunctionthespeedatwhichyoudrive


Why?

13.! = 7!!


Why?

14.Eachpointonthegraphisexactly1/3ofthepreviouspoint.


Why?

17




15.! 1 = 7, ! 2 = 7, ! ! = ! ! − 1 + !(! − 2)


Why?

16.

! 1 = 1, ! ! = 23 !(! − 1)


Why?

18




2.3 Linear, Exponential or Neither? – Teacher Notes

A Practice Understanding Task

Purpose:

Thepurposeofthistaskistodevelopfluencyindeterminingifafunctionislinearorexponentialusingvarious

representations.Thetaskalsoprovidesopportunitiesfordiscussionoffeaturesofthefunctionsbaseduponthe

representationgiven.

CoreStandardsFocus:

F-LE1:Distinguishbetweensituationsthatcanbemodeledwithlinearfunctionsandwithexponentialfunctions.

F-LE2:Constructlinearandexponentialfunctions,includingarithmeticandgeometricsequences,givenagraph,a

descriptionofarelations,ortwoinput-outputpairs(includereadingthesefromatable).

a. Provethatlinearfunctionsgrowbyequaldifferencesoverequalintervals,andthatexponentialfunctions

growbyequalfactorsoverequalintervals.

b. Recognizesituationsinwhichonequantitychangesataconstantrateperunitintervalrelativetoanother.

c. Recognizesituationsinwhichaquantitygrowsordecaysbyaconstantpercentrateperunitinterval

relativetoanother.

StandardsforMathematicalPracticeofFocusintheTask:

SMP6–Attendtoprecision.

SMP7–Lookforandmakeuseofstructure.

TheTeachingCycle:

Launch(WholeClass):

Refertheclasstothelinearandexponentialchartsmadeintheprevioustask.Inthistasktheywillbelookingata

numberoffunctions,somelinear,someexponential,someneither.Theyneedtoidentifywhatkindoffunctionis

shownineachproblemandprovidetworeasonsfortheiranswers.Onereasonmaybefairlyeasy,baseduponthe

chart,thesecondonewillrequirethemtostretchalittle.




Explore(SmallGroup):

Duringthesmallgroupwork,listenforproblemsthataregeneratingcontroversy.Ifstudentsfeelthataparticular

problemistoovague,askthemwhatinformationwouldbenecessaryforthemtodecideandwhythatinformation

isimportant.

Discuss(WholeClass):

Startthediscussionbygoingthrougheachproblemandaskingagrouptosayhowtheycategorizeditandwhy.

Aftereachproblem,askiftherewasanydisagreementorifanothergroupcouldaddanotherreasontosupportthe

category.Ifthereisdisagreement,askstudentstopresenttheirargumentsmoreformallyandaddatleastone

representationtosupporttheirclaim.Theemphasisofthediscussionshouldbetorecognizetheconstantrateof

changetodefinealinearfunctionandtheequalfactorsoverequalintervalsthatdefineanexponentialfunction.Be

surethattheclassdiscussionincludesatable,agraph,anequation,andadescriptionorstorycontextforboth

linearandexponentialfunctions.

AlignedReady,Set,Go:LinearandExponentialFunctions2.3

SECONDARY MATH I // MODULE 2


Mathematics Vision Project

Licensed under the Creative Commons Attribution CC BY 4.0

mathematicsvisionproject.org

2.3

READY Topic:Comparingratesofchangeinbothlinearandexponentialsituations.Identifywhethersituation“a”orsituation“b”hasagreaterrateofchange.

1. x y

-10 -48

-9 -43

-8 -38

-7 -33

a.

b.

2. a.

b.

3. a.Leehas$25withheldeachweekfromhissalarytopayforhissubwaypass.

b.Joseoweshisbrother$50.Hehaspromisedtopayhalfofwhatheoweseachweekuntilthedebtispaid.

4. a.

x 6 10 14 18

y 13 15 17 19

b.Thenumberofrhombiineachshape.

Figure1Figure2Figure3

5. a.! = 2(5)! b.Inthechildren'sbook,TheMagicPot,everytimeyouputoneobjectintothepot,twoofthesameobjectcomeout.Imaginethatyouhave5magicpots.

READY, SET, GO! Name PeriodDate

-5

-5

5

5

19






2.3

SET Topic:Recognizinglinearandexponentialfunctions.Basedoneachofthegivenrepresentationsofafunctiondetermineifitislinear,exponentialorneither.6.Thepopulationofatownisdecreasingatarateof1.5%peryear.

7.Joanearnsasalaryof$30,000peryearplusa4.25%commissiononsales.

8.3x+4y=-3

9.Thenumberofgiftsreceivedeachdayof”The12DaysofChristmas”asafunctionoftheday.(“Onthe4thdayofChristmasmytruelovegavetome,4callingbirds,3Frenchhens,2turtledoves,andapartridgeinapeartree.”)

10.

11.

Sideofasquare Areaofasquare1inch 1in22inches 4in2

3inches 9in2

4inches 16in2

GO Topic:GeometricmeansForeachgeometricsequencebelow,findthemissingtermsinthesequence.

12. 13. 14.

x 1 2 3 4 5

y 2 162

x 1 2 3 4 5

y 1/9 -3

x 1 2 3 4 5

y 10 0.625

20






2.3

15. 16. Findtherateofchange(slope)ineachoftheexercisesbelow.

17. x g(x)

-5 11

-3 4

-2 0.5

0 -6

18. t h(t)

3 13

8 23

18 43

23 53

19.

n f(n)

-7 20

-5 24

-1 32

2 38

20. (2,5)(8,29) 21. 22. (-3,7)(8,29)

x 1 2 3 4 5

y g gz4

x 1 2 3 4 5

y -3 -243

21

Documents

2.3 Linear, Exponential or Neither? d A - Utah Education … MATH 1 // MODULE 2 LINEAR & EXPONENTIAL FUNCTIONS – 2.3 Mathematics Vision Project Licensed under the Creative Commons