Home on the Range Part 1

Home on the Range Part 1

Indicatetheanswerchoicethatbestcompletesthestatementoranswersthequestion.

Expresseachrelationasagraphandamapping.Thendeterminethedomainandrange.

1.{(1,–2),(–2,–3),(2,4),(1,–4)}

a.

D={–2,1,2};R={–4,–3,–2,4}

b.

D={–2,1,2,4};R={–4,–3,–2}

c.

D={–2,1,2};R={–4,–3,–2,4}

d.

D={–2,1,2};R={–4,–3,–2,4}

Asoftdrinkbottlefillingmachinecanfill22bottlesperminute.Thetableshowstherelationshipbetweenthenumberofminutesandthenumberofbottlesfilled.

Time(minutes) / 1 / 2 / 3 / 4 / 5
Bottlesfilled / 22 / 44 / 66 / 88 / 110

2.Usethesoftdrinkbottletabletopredicthowmanybottleswillbefilledaftersevenminutes.

a.154bottles

b.144bottles

c.176bottles

d.150bottles

____3. Expresstherelationshownineachtable,mapping,orgraphasasetoforderedpairs.Thendeterminethedomainandrange.

x / y
0 / 0
5 / 2
10 / 6.5
15 / 9
20 / 11.5

4.____

11.Acompanyincreasesthesalariesofitsemployeeseveryyearby15%.Thegraphshowsthesalaryofaparticularemployeeasthenumberofyearsincrease.

Doesthegraphrepresentafunction?Explain.Describehowreal-worldsituationscanbemodeledusinggraphsandfunctions.

1. Findtheinverseoftherelation.

{(6,–3),(5,1),(4,–10),(–8,7)}

Graphthevariationifyvariesinverselyasx.

6 .when

a.b.

c.d.

Solvetheproblemofexponentialgrowth.

7.Acompanyhadaprofitof$823,500in2010.Thisisa26%increasefrom2005.Whatwasthecompany'sprofitin2005? Roundtothenearesthundred.

a.$653,600b.$802,300c.$1,037,600d.$572,900

Translatethesentenceintoanequation.

8.Threetimesthesumofaandbisequaltofivetimesc.a.

b.

c.

d.

1. Theairtrafficcontrollerschedulesthetakeofftimeof5flightsinanhouratanairport.

Flight / Time(P.M.)
Flight1 / 12:10
Flight2 / 12:20
Flight3 / 12:30
Flight4 / 12:40
Flight5 / 12:50

a.Howarerationalequationsimportantintheoperationofflightsattheairports?

b.Includeinyouransweranexplanationofhowrationalequationscanbeusedtoapproximatethetimethatplaneswillpasseachotheriftheyleavedistantairportsandheadtowardseachother.

______

1. Arectangleis8meterswideand12meterslong.Findtheheightofatrianglewithabase6meterslongandanareaequaltothatoftherectangle.

Indicatetheanswerchoicethatbestcompletesthestatementoranswersthequestion.

Graphthefunction.Findthey-interceptandstatethedomainandrange.

11..

a.b.

y-intercept=1

domain:allrealnumbersrange:y0

c.

y-intercept=4

domain:allrealnumbersrange:y0

y-intercept=1

domain:allrealnumbersrange:y0

d.

y-intercept=3

domain:allrealnumbersrange:y0

Pick the correct graph for

12.f(x)= 2√x +4

a.b.

c.d.

13. Describethetransformationfromtheparentfunctionandstatethedomainandrange.

5.

______

14.Thisyear,aschooldistricthasabudgetof$58million.Theschoolboardhasvotedtoincreasethebudgetbyonly1.1%eachyear.

a.Explainhowtheexponentialgrowthcanbeusedtopredictthefuturebudget.

b.Explaintheequation.

c.Estimatetheschoolbudgetafter10years.

______

15. Writethefunctionandstatethedomainandrange.

______

. Indicatetheanswerchoicethatbestcompletesthestatementoranswersthequestion.

Graphtherationalfunction.

16.f(x)=

a.b.

c.

d.

17.WhenMarkwas2yearsold,hisparentsinvested$2000inamoneymarketaccountwithannualaverageinterestrateof8%.After15years,howmuchmoneywillhehaveintheaccount?

____ 18. Graph the following y–2+–2

a.b.

c.d.

19. AccordingtotheU.S.CensusBureau,thepopulationofCaliforniain2010was37.3million.Thisisa10.4%increaseoverthe2000count.Assumingthiscontinuedwhatwouldthepopulationbein2030?

a.50.2 millionb.41.2 million

c.45.5 milliond.42.9 million

20.Aboxismadefromarectangularmetalsheetbycuttingfourequalsquaresfromthecorners.Thedimensionsoftheboxareshownbelow.Writeanequationfortheareaofthesheetrequiredtomakethebox.

____21 .Findthefirstfivetermsofthesequenceinwhicha1=12andan=–2an–1+4,ifn≥2.

a.–20,44,–84,172,–340

b.2,0,–2,–4,–6

c.28,12,–20,44,–84

d.12,–20,44,–84,172

22. Thetableshowstheamountofmoneyinasavingsaccountafterseveralweeks.

Week / Savings
1 / $125
2 / $140
3 / $155
4 / $170
5 / $185
6 / $200

a.Isthesequencearithmeticorgeometric?Explain.Findthecommondifferenceorcommonratio.

b.Writearecursiveformulaforthesequence.

c.Writeanexplicitformulaforthesequence.

23. Writearecursiveformulaforan=–8n+7.