SECONDARY MATH II // MODULE 4

MORE FUNCTIONS, MORE FEATURES - 4.3

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

4.3 More Features, More Functions

A Solidify Understanding Task

PartI

MichellelikesridingherbiketoandfromherfavoritelakeonWednesdays.Shecreatedthe

followinggraphtorepresentthedistancesheisawayfromthelakewhilebiking.

1. InterpretthegraphbywritingthreeobservationsaboutMichelle’sbikeride.

2. Writeapiecewisefunctionforthissituation,witheachlinearfunctionbeinginpoint-slopeformusingthepoint(3,0).Whatdoyounotice?

3. Thisparticularpiecewisefunctioniscalledalinearabsolutevaluefunction.Whatarethetraitsyouarenoticingaboutlinearabsolutevaluefunctions?

Time(inminutes)

Distance(inblocks)

CCBYHy

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https://pixabay.com/pho

to-

1777

917/

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SECONDARY MATH II // MODULE 4

MORE FUNCTIONS, MORE FEATURES - 4.3

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

PartII

Inthispartofthetask,youwillsolidifyyourunderstandingofpiecewiseanduseyourknowledgeof

transformationstomakesenseofabsolutevaluefunctions.Followthedirectionsandanswerthe

questionsbelow.

4. Graphthelinearfunction! ! = !.

5. Onthesamesetofaxes,graph ! ! = ! ! .

6. Explainwhathappensgraphicallyfrom! ! !" ! ! .

7. Writethepiecewisefunctionfor! ! .Explainyourprocessforcreatingthispiecewisefunctionandhowitconnectstoyouranswerinquestion3.

8. Completethetableofvaluesfrom[-4,4]forf(x)andg(x).Explainhowthisconnectstoyouranswerinquestions3and4.

x f(x) g(x)-4 -3 -2 -1 0 1 2 3 4

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SECONDARY MATH II // MODULE 4

MORE FUNCTIONS, MORE FEATURES - 4.3

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

PartIII

9. Thegraphbelowisanotherexampleofanabsolutevaluefunction.Theequationofthisfunctioncanbewrittentwoways:asanabsolutevaluefunction:! ! = ! + 3 orasapiecewise:! ! = −(! + 3), ! < −3

(! + 3), ! ≥ −3

Howdothesetwoequationsrelatetoeachother?

Belowaregraphsandequationsofmorelinearabsolutevaluefunctions.Writethepiecewisefunctionforeach.Seeifyoucancreateastrategyforwritingtheseequations.

10. Abolutevalue:! ! = ! − 1 + 2

Piecewise: ! ! =

11.

Abolutevalue:! ! = ! + 2

Piecewise: ! ! =

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SECONDARY MATH II // MODULE 4

MORE FUNCTIONS, MORE FEATURES - 4.3

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

Graphthefollowinglinearabsolutevaluepiecewisefunctions.

12. ! ! = ! − 4 = −(! − 4), ! < 4(! − 4), ! ≥ 4 13.! ! = ! + 1 = − ! + 1, ! < 0

! + 1, ! ≥ 0

14.

Piecewise:! ! = −3 ! + 2 + 1, ! < −23 ! + 2 + 1, ! ≥ −2

AbsoluteValue:! ! =

15.Explainyourmethodfordoingthefollowing:

a) Writingpiecewiselinearabsolutevaluefunctionsfromagraph.

b) Writingpiecewiselinearabsolutevaluefunctionsfromanabsolutevaluefunction.

c) Graphingabsolutevaluefunctions(fromeitherapiecewiseoranabsolutevalueequation).

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