CH.4, L2– WRITING EXPLICIT AND RECURSIVE FUNCTIONS › uploads › 8 › 5 › 5 › 8 ›...

Integrated Math I Name: ________________________________________ Period: ______ Date: ____________

CFS:1. Sequenceisannotatedforgrowthrateorratio2. Recursivefunctionshaveinitialvalueandrecursiverule3. Explicitfunctionsareinlinearorexponentialequations

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CH.4, L2– WRITING EXPLICIT AND RECURSIVE FUNCTIONS Objective:Givenasequence,Iwillcreatearecursiveorexplicitformulabyidentifyingtheinitialtermandgrowthrateorratio.ThinkAboutIt:Ascholartookthesequencebelowandorganizeditintoatablewheretheoutputsweredefinedasthenumbersinthesequenceusing𝑎(𝑛)andtheinputswerethepositioninthesequence,𝑛.Forexample,𝑎 3 = 7impliesthatthethirdterminthesequenceis7.Knowingthis,answerthefollowingquestions

3,5,7,9,11,…

a) Whatisthefirsttermandhowwouldyourepresentitusingfunctionnotation𝑎(𝑛)?________________________________________________________________________b) Explainhowyouwouldfindthevaluethe25thtermifyouknewthevalueofthe24th

term.________________________________________________________________________________________________________________________________________________c) Writealinearorexponentialequationthatrepresentsthefunction.__________________________________________________________

Keywords: sequence, explicit, recursive

Big Idea:

KeyPoint:

KeyPoint:

Integrated Math I Name: ________________________________________ Period: ______ Date: ____________

CFS:1. Sequenceisannotatedforgrowthrateorratio2. Recursivefunctionshaveinitialvalueandrecursiverule3. Explicitfunctionsareinlinearorexponentialequations

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InteractionwithNewMaterial:

Ex.1) Whichofthefollowingrecursivefunctionsrepresentsthegraphshown?

a. 𝑎 0 = 0.5, 𝑎 𝑛 = 𝑎 𝑛 − 1 + 1.5 b. 𝑎 1 = 0.5, 𝑎 𝑛 = 𝑎 𝑛 + 1.5 c. 𝑎 1 = 0.5, 𝑎 𝑛 = 𝑎 𝑛 − 1 + 1.5 d. 𝑎 1 = −1, 𝑎 𝑛 = 𝑎 𝑛 − 1 + 1.5

Ex.2)Giventhesequence,writearecursiveandexplicitfunctionrepresentingit.

½,1,2,4,8,…

Integrated Math I Name: ________________________________________ Period: ______ Date: ____________

CFS:1. Sequenceisannotatedforgrowthrateorratio2. Recursivefunctionshaveinitialvalueandrecursiverule3. Explicitfunctionsareinlinearorexponentialequations

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PartnerPractice:(LowDifficulty)1. Writetherecursivefunctionforthefollowingsequences:

a. 1,3,5,7,9

b. 1,3,9,27,81

2. Writetheexplicitfunctionandtherecursivefunctionforthefollowingsequence:

45,39,33,27,21,…

3. Createatableofvaluesinordertowritearecursiveandexplicitfunctionthatrepresentsthegraphbelow.

Integrated Math I Name: ________________________________________ Period: ______ Date: ____________

CFS:1. Sequenceisannotatedforgrowthrateorratio2. Recursivefunctionshaveinitialvalueandrecursiverule3. Explicitfunctionsareinlinearorexponentialequations

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PartnerPractice:(MediumDifficulty)

4. Writeanexplicitandrecursivefunctionforthetableandaccompanyinggraphbelow.Explainhowtheshapeofthegraphletsyouknowwhattypeoffunctiontowrite.

5. RegentsProblem!

Integrated Math I Name: ________________________________________ Period: ______ Date: ____________

CFS:1. Sequenceisannotatedforgrowthrateorratio2. Recursivefunctionshaveinitialvalueandrecursiverule3. Explicitfunctionsareinlinearorexponentialequations

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6. RegentsProblem!-Answerthequestionbelowandidentifyiftheequationisexplicitorrecursive.Writetheotherformoftheequation(e.g.iftheequationsbelowarerecursive,writeanexplicitequationorviceversa).

PartnerPractice:(HardDifficulty)

7. Forthefunctionsbelow;ifitisexplicit,writetheequivalentrecursivefunction.Ifitisrecursive,writetheexplicitfunction.

a) 𝑎 𝑛 = 3𝑛 − 1

b) 𝑎 1 = 2, 𝑎 𝑛 = 2 𝑎(𝑛 − 1

Integrated Math I Name: ________________________________________ Period: ______ Date: ____________

CFS:1. Sequenceisannotatedforgrowthrateorratio2. Recursivefunctionshaveinitialvalueandrecursiverule3. Explicitfunctionsareinlinearorexponentialequations

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