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 Part I Michelle likes riding her bike to and from her favorite lake on Wednesdays. She created the following graph to represent the distance she is away from the lake while biking. 1. Interpret the graph by writing three observations about Michelle’s bike ride. 2. Write a piecewise function for this situation, with each linear function being in point-slope form using the point (3,0). What do you notice? 3. This particular piecewise function is called a linear absolute value function. What are the traits you are noticing about linear absolute value functions? Time (in minutes) Distance (in blocks) CC BY HynoArt https://pixabay.com/photo- 1777917/ 11
Transcript of 4.3 More Features, More t Functions...
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
noArt
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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