SECONDARY MATH I // MODULE 3

FEATURES OF FUNCTIONS – 3.6

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3.6

READY Topic:SolvingSystemsbySubstitutionInpriorworkthemeaningof! ! = ! ! wasdiscussed.Thismeanstofindthepointwherethetwoequationsareequalandwherethetwographsintersect.Itispossibletofindthepointofintersectionalgebraicallyinsteadofgraphingthetwolines.Since! ! = ! ! ,it’spossibletoseteachequationequaltotheotherandsolveforx.

Example:Findthepointofintersectionoffunction! ! = 3! + 4andfunction! ! = 4! + 1.Since,! x = g x , !"# 3! + 4 = 4! + 1.Thensolveforx.

3! + 4 = 4! + 1 Subtract3xand1frombothsidesoftheequation.−3! − 1 = −3! − 10! + 3 = 1! + 0 3 = 1!Nowletx=3ineachequationtofind! ! !"# ! ! !ℎ!" ! = 3. ! 3 = 3 3 + 4 → 9 + 4 = 13 !"#! 3 = 4 3 + 1 → 12 + 1 = 13When! = 3, ! 3 !"# ! 3 !"#ℎ !"#$% 13. !ℎ! !"#$% !" !"#$%&$'#!(" !" 3, 13 .

Findthepointofintersectionfor! ! !"# ! ! usingthealgebraicmethodintheexampleabove.1.! ! = −5! + 12and! ! = −2! − 3

2.! ! = !! ! + 2and! ! = 2! − 7

3.! ! = − !! ! + 5and! ! = −! + 7

4.! ! = ! − 6and! ! = −! − 6

READY, SET, GO! Name PeriodDate

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SECONDARY MATH I // MODULE 3

FEATURES OF FUNCTIONS – 3.6

Mathematics Vision Project

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3.6

SET Topic:DescribingattributesofafunctionsbasedongraphicalrepresentationUsethegraphofeachfunctionprovidedtofindtheindicatedvalues.

5.f(x)

a.f(4)=________b.f(-4)=__________

c.f(x)=4,x=_________d.f(x)=7,x=________

6.g(x)

a.g(-1)=__________b.g(-3)=___________

c.g(x)=-4x=_______d.g(x)=-1,x=_________

7.h(x)

a.h(0)=________b.h(3)=__________

c.h(x)=1,x=_________d.h(x)=-2,x=______

8.d(x)

a.d(-5)=________b.d(4)=__________

c.d(x)=4,x=_________d.d(x)=0,x=______

6

4

2

–2

–5 5

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SECONDARY MATH I // MODULE 3

FEATURES OF FUNCTIONS – 3.6

Mathematics Vision Project

Licensed under the Creative Commons Attribution CC BY 4.0

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3.6

Foreachsituationeithercreateafunctionorusethegivenfunctiontofindandinterpretsolutions.9.Francollecteddataonthenumberoffeetshecouldwalkeachsecondandwrotethefollowingruletomodelherwalkingrate! ! = 4!.

a.WhatisFranlookingforifshewrites! 12 = _______?

b.Inthissituationwhatdoes! ! = 100tellyou?

c.Howcanthefunctionrulebeusedtoindicateatimeof16secondswaswalked?

d.Howcanthefunctionrulebeusedtoindicatethatadistanceof200feetwaswalked? 10.Mr.Multbankhasdevelopedapopulationgrowthmodelfortherodentsinthefieldbyhishouse.Hebelievesthatstartingeachspringthepopulationcanbemodeledbasedonthenumberofweekswiththefunction! ! = 8 2! .

a.Find! ! = 128.

b.Find! 4 .

c.Find! 10 .

d.Findthenumberofweeksitwilltakeforthepopulationtobeover20,000.e.Inayearwith16weeksofsummer,howmanyrodentswouldheexpectbytheendofthesummerusingMr.Multbank’smodel?Whataresomefactorsthatcouldchangetheactualresultfromyourestimate?

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SECONDARY MATH I // MODULE 3

FEATURES OF FUNCTIONS – 3.6

Mathematics Vision Project

Licensed under the Creative Commons Attribution CC BY 4.0

mathematicsvisionproject.org

3.6

GO Topic:Describefeaturesoffunctionsfromthegraphicalrepresentation.Foreachgraphgivenprovideadescriptionofthefunction.Besuretoconsiderthefollowing:decreasing/increasing,min/max,domain/range,etc.11. Descriptionoffunction:

12. Descriptionoffunction:

13. Descriptionoffunction:

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