2.6Form Follows Function - Mr. Lemon's Math Websitelemonmath.weebly.com/uploads/1/0/6/6/10667663/2.6...2.6 Form Follows Function A Practice Understanding Task In our work so far, we

SECONDARY MATH 1 // MODULE 2

LINEAR & EXPONENTIAL FUNCTIONS – 2.6

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2.6 Form Follows Function

A Practice Understanding Task

Inourworksofar,wehaveworkedwithlinearand

exponentialequationsinmanyforms.Someofthe

formsofequationsandtheirnamesare:

LinearFunctionsEquation Name

𝑦 =12𝑥 + 1

SlopeInterceptForm𝑦 = 𝑚𝑥 + 𝑏,wheremistheslopeandbisthe

y-intercept

𝑦 =12

𝑥 − 4 + 3

PointSlopeForm𝑦 = 𝑚 𝑥 − 𝑥! + 𝑦!,wheremistheslopeand(x1,y1)thecoordinatesofapointontheline

𝑓 0 = 1, 𝑓 𝑛 = 𝑓 𝑛 − 1 +12

RecursionFormula𝑓 𝑛 = 𝑓 𝑛 − 1 +D,

Givenaninitialvaluef(a)D=constantdifferenceinconsecutiveterms

(usedonlyfordiscretefunctions)

ExponentialFunctionsEquation Name

𝑦 = 10(3)! ExplicitForm𝑦 = 𝑎(𝑏)!

𝑓 0 = 10, 𝑓 𝑛 + 1 = 3𝑓 𝑛

RecursionFormula𝑓 𝑛 + 1 = 𝑅𝑓 𝑛

Givenaninitialvaluef(a)R=constantratiobetweenconsecutiveterms

(usedonlyfordiscretefunctions)

CCBYPaulDow

ney

https://flic.kr/p/ta4a





Knowinganumberofdifferentformsforwritingandgraphingequationsislikehavinga

mathematicaltoolbox.Youcanselectthetoolyouneedforthejob,orinthiscase,theformofthe

equationthatmakesthejobeasier.Anymasterbuilderwilltellyouthatthemoretoolsyouhave

thebetter.Inthistask,we’llworkwithourmathematicaltoolstobesurethatweknowhowtouse

themallefficiently.Asyoumodelthesituationsinthefollowingproblems,thinkaboutthe

importantinformationintheproblemandtheconclusionsthatcanbedrawnfromit.Isthe

functionlinearorexponential?Doestheproblemgiveyoutheslope,apoint,aratio,ay-intercept?

Isthefunctiondiscreteorcontinuous?Thisinformationhelpsyoutoidentifythebesttoolsandget

towork!

1. Inhisjobsellingvacuums,Joemakes$500eachmonthplus$20foreachvacuumhesells.WritetheequationthatdescribesJoe’smonthlyincomeIasafunctionofthen,thenumberofvacuumssold.

Nametheformoftheequationyouwroteandwhyyouchosetousethatform.

Thisfunctionis: linear exponential neither (chooseone)

Thisfunctionis: continuous discrete neither (chooseone)

2. Writetheequationofthelinewithaslopeof-1throughthepoint(-2,5)Nametheformoftheequationyouwroteandwhyyouchosetousethatform.







3.Writetheequationofthegeometricsequencewithaconstantratioof5andafirsttermof-3.




4. Writetheequationofthefunctiongraphedbelow:




5. ThepopulationoftheresorttownofJavaHotSpringsin2003wasestimatedtobe35,000

peoplewithanannualrateofincreaseofabout2.4%.Writetheequationthatmodelsthe

numberofpeopleinJavaHotSprings,witht=thenumberofyearsfrom2003?








6. Yessica’ssciencefairprojectinvolvedgrowingsomeseedstoseewhatfertilizermadethe

seedsgrowfastest.Oneideashehadwastouseanenergydrinktofertilizetheplant.(She

thoughtthatiftheymakepeopleperky,theymighthavethesameeffectonplants.)Thisis

thedatathatshowsthegrowthoftheseedeachweekoftheproject.

Week 1 2 3 4 5

Height(cm) 1.7 2.9 4.1 5.3 6.5

Writetheequationthatmodelsthegrowthoftheplantovertime.




Anequationgivesusinformationthatwecanusetographthefunction.Pickouttheimportant

informationgivenineachofthefollowingequationsandusetheinformationtographthefunction.

7. 𝑦 = !!𝑥 − 5

Whatdoyouknowfromtheequationthathelpsyoutographthefunction?





8. 𝑦 = 2!

9. 𝑦 = −2 𝑥 + 6 + 8

9. 𝑓 1 = −5, 𝑓 𝑛 = 𝑓 𝑛 − 1 + 1




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2.6Form Follows Function - Mr. Lemon's Math Websitelemonmath.weebly.com/uploads/1/0/6/6/10667663/2.6...2.6 Form Follows Function A Practice Understanding Task In our work so far, we