4.3 more features, more t functions...
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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
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)
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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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