3.5 Pooling it Together - Math with Ms....
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SECONDARY MATH I // MODULE 3 FEATURES OF FUNCTIONS Mathematics Vision Project Licensed under the Creative Commons Attribution CC BY 4.0 mathematicsvisionproject.org 3.5 Pooling it Together A Solidify Understanding Task Aly and Dayne work at a water park and have to drain the water at the end of each month for the ride they supervise. Each uses a pump to remove the water from the small pool at the bottom of their ride. The graph below represents the amount of water in Aly’s pool, a(x), and Dayne’s pool, d(x), over time. In this scenario, they decided to work together to drain their pools and created the equation: g(x) = a(x) +d(x). Answer the following questions about g(x). 1. What does g(x) represent? 2. Create the graph of g(x) on a new set of axes using the graphs of a(x) and d(x). Identify g(x) and label (scale, axes). Amount of water (gallons) 4,000 5 CC BY Hanumann https://flic.kr/p/7tZHkq 1 Homework help at www.rsgsupport.org 127
Transcript of 3.5 Pooling it Together - Math with Ms....
SECONDARY MATH I // MODULE 3
FEATURES OF FUNCTIONS
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
3.5 Pooling it Together A Solidify Understanding Task
AlyandDayneworkatawaterparkandhavetodrainthewaterattheendofeachmonthfortheridetheysupervise.Eachusesapumptoremovethewaterfromthesmallpoolatthebottomoftheirride.ThegraphbelowrepresentstheamountofwaterinAly’spool,a(x),andDayne’spool,d(x),overtime.Inthisscenario,theydecidedtoworktogethertodraintheirpoolsandcreatedtheequation:
g(x)=a(x)+d(x).
Answerthefollowingquestionsaboutg(x).
1. Whatdoesg(x)represent?
2. Createthegraphofg(x)onanewsetofaxesusingthegraphsofa(x)andd(x).Identifyg(x)andlabel(scale,axes).
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Homework help at www.rsgsupport.org 127
SECONDARY MATH I // MODULE 3
FEATURES OF FUNCTIONS
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
3. Writetheequationforthefunctiong(x)usingthegraphyoucreated.Comparethisequationtothealgebraicrepresentationoffindingthesumoftheequationsfora(x)andd(x).(Theequationswerecreatedinthelasttask,“TheWaterPark”task).
4. Shouldthealgebraicequationofg(x)bethesameasthealgebraicfunctioncreatedfromthegraph?Whyorwhynot?
5. Useboththegraphicalaswellasthealgebraicrepresentationtodescribecharacteristicsofg(x)andexplainwhateachcharacteristicmeans(eachintercept,domainandrangeforthissituationandfortheequation,maximaandminima,whetherornotg(x)isafunction,etc.)
6. Explainwhyaddingthetwovaluesofthey-interceptstogetherina(x)andd(x)canbeusedtofindthey-intercepting(x).
7. Canasimilarmethodbeusedtofindthex-intercepts?Explain.
Homework help at www.rsgsupport.org 128
