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  • CH.4, L2– WRITING EXPLICIT AND RECURSIVE FUNCTIONS › uploads › 8 › 5 › 5 › 8 › 85588… · 2. Recursive functions have initial value and recursive rule 3. Explicit functions
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Integrated Math I Name: ________________________________________ Period: ______ Date: ____________ CFS: 1. Sequence is annotated for growth rate or ratio 2. Recursive functions have initial value and recursive rule 3. Explicit functions are in linear or exponential equations 1 CH.4, L2– WRITING EXPLICIT AND RECURSIVE FUNCTIONS Objective: Given a sequence, I will create a recursive or explicit formula by identifying the initial term and growth rate or ratio. Think About It: A scholar took the sequence below and organized it into a table where the outputs were defined as the numbers in the sequence using () and the inputs were the position in the sequence, . For example, 3 = 7 implies that the third term in the sequence is 7. Knowing this, answer the following questions 3, 5, 7, 9, 11, … a) What is the first term and how would you represent it using function notation ()? ________________________________________________________________________ b) Explain how you would find the value the 25 th term if you knew the value of the 24 th term. ________________________________________________________________________ ________________________________________________________________________ c) Write a linear or exponential equation that represents the function. __________________________________________________________ Keywords: sequence, explicit, recursive Big Idea: Key Point: Key Point:

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Page 1: CH.4, L2– WRITING EXPLICIT AND RECURSIVE FUNCTIONS › uploads › 8 › 5 › 5 › 8 › 85588… · 2. Recursive functions have initial value and recursive rule 3. Explicit functions

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

CFS:1. Sequenceisannotatedforgrowthrateorratio2. Recursivefunctionshaveinitialvalueandrecursiverule3. Explicitfunctionsareinlinearorexponentialequations

1

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:

Page 2: CH.4, L2– WRITING EXPLICIT AND RECURSIVE FUNCTIONS › uploads › 8 › 5 › 5 › 8 › 85588… · 2. Recursive functions have initial value and recursive rule 3. Explicit functions

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

CFS:1. Sequenceisannotatedforgrowthrateorratio2. Recursivefunctionshaveinitialvalueandrecursiverule3. Explicitfunctionsareinlinearorexponentialequations

2

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,…

Page 3: CH.4, L2– WRITING EXPLICIT AND RECURSIVE FUNCTIONS › uploads › 8 › 5 › 5 › 8 › 85588… · 2. Recursive functions have initial value and recursive rule 3. Explicit functions

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

CFS:1. Sequenceisannotatedforgrowthrateorratio2. Recursivefunctionshaveinitialvalueandrecursiverule3. Explicitfunctionsareinlinearorexponentialequations

3

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.

Page 4: CH.4, L2– WRITING EXPLICIT AND RECURSIVE FUNCTIONS › uploads › 8 › 5 › 5 › 8 › 85588… · 2. Recursive functions have initial value and recursive rule 3. Explicit functions

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

CFS:1. Sequenceisannotatedforgrowthrateorratio2. Recursivefunctionshaveinitialvalueandrecursiverule3. Explicitfunctionsareinlinearorexponentialequations

4

PartnerPractice:(MediumDifficulty)

4. Writeanexplicitandrecursivefunctionforthetableandaccompanyinggraphbelow.Explainhowtheshapeofthegraphletsyouknowwhattypeoffunctiontowrite.

5. RegentsProblem!

Page 5: CH.4, L2– WRITING EXPLICIT AND RECURSIVE FUNCTIONS › uploads › 8 › 5 › 5 › 8 › 85588… · 2. Recursive functions have initial value and recursive rule 3. Explicit functions

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

CFS:1. Sequenceisannotatedforgrowthrateorratio2. Recursivefunctionshaveinitialvalueandrecursiverule3. Explicitfunctionsareinlinearorexponentialequations

5

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

Page 6: CH.4, L2– WRITING EXPLICIT AND RECURSIVE FUNCTIONS › uploads › 8 › 5 › 5 › 8 › 85588… · 2. Recursive functions have initial value and recursive rule 3. Explicit functions

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

CFS:1. Sequenceisannotatedforgrowthrateorratio2. Recursivefunctionshaveinitialvalueandrecursiverule3. Explicitfunctionsareinlinearorexponentialequations

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