LinearFunctionVocabulary:Directions:asyoutraveltoeachstationincludeanexampleofeachvocabularywordbelow

Usethefollowingpointstocreateexamplesfortheboldedwordstocreateexamples.(-2,3),(8,5),(-8,3),(0,0),(5,0)

Vocabularyword: Definition: Examples:Domain(input) Allthexvalues

Range(output) Alltheyvalues

Relation Arelationisafancywordforasetoforderedpairs

Orderedpairs Thexandyvalueofapointonacoordinategraph

Function Whereeveryxvaluehasonlyoney

valueYESORNO

Mapping Theideaofpairingeachmemberofthe

domainwitheachmemberoftherange

Increasing Goesupfromlefttorightonagraph Picture:

Decreasing Goesdownfromlefttorightonagraph Picture:

Center1:

HowtotellifitisafunctionorisNOTafunction:

Wedowhatiscalledtheverticallinetest.IfIdrawaverticallineanywhereonthegraphbelow,willIpassthroughthe

samepointmorethanonce?(greenlinesrepresentmytestlines)

ThisoneeachlineonlyhasonereddotsoYESitisa

function.

ThisoneeachlineonlyhasmorethanonereddotsoNOitisNOTafunction.

Youtry:Lookatthegraphsbelow,isitorisitnotafunction?Center2:

1.

2.

3.

4.

5.

6.

Mapping:HowtotellifitisafunctionorisNOTafunction:Mappingisastrategyusedtotellwhetherornotarelationisa

functionornotafunction.Thex’sgoinonecircle,they’sinanother.Iamthengoingtoconnectthelinestomakesureeachnumberhasonlyonelineconnectingittoanothernumber.DoNOTrepeatnumbersofthesameletterinacircle.Ex.iftherearetwox’swiththevalueof3,

youonlywriteone2.

Function:Whereeveryxvaluehasonlyoneyvalue

0

-1

4

5

-8

3

5

-9

0

-3

Relation:(0,3),(-1,5),(4,0),(5,-9),(-8,-3)

Yesthisisafunction.

Relation:(0,3),(-1,5),(0,0),(5,-9),(-8,5)

NOthisisNOTafunction.

0

-1

5

-8

3

5

-9

0

YIKES!!!!Morethanonexispairedwith

oney.

Relation:(-1,3),(-2,0),(5,0),(5,-9),(-3,5)

Relation:(0,2),(-1,7),(3,0),(2,-9),(-9,4)

Relation:(0,1),(-1,4),(8,0),(0,2),(-8,-2)

YOUtry!

Center3:

Domain(input)/andRange(output)

Giventhefollowingequationfindthevaluesofy.

y=2x-5

Giventhefollowingequationfindthevaluesofy.

y=-6x+1

Giventhefollowingequationfindthevaluesofy.

y=-x-2

x y-2 y=2(-2)-5 -9

0 y=2(0)-5 -5

5

4

-3

1

x y-4

0

-2

4

-0.5

1

x y-3

0

-1

-4

3

1

Listyourrange(yvaluesforthisfunction): Listyourrange(yvaluesforthisfunction): Listyourrange(yvaluesforthisfunction):

Domain:(-3,-2,0,1,4,5) Domain:(-4,-2,-0.5,0,1,4) Domain:(-4,-3,-1,0,1,3)

Center4:

Domain(input)/andRange(output)Giventhefollowingequationfind

thevaluesofx.

y=2x-6

Giventhefollowingequationfindthevaluesofx.

y=x+1

Giventhefollowingequationfindthevaluesofx.

y=-x-2

x y-1 (-8)=2x–6

+6+6-2=2x22-1=x

-8

4 2=2x-6 2

0

-1

4

-2

x y 9

-5

3

0

-1

4

x y -3

5

-1

0

2

6

Listyourdomain(xvaluesforthisfunction):

Listyourdomain(xvaluesforthisfunction): Listyourdomain(xvaluesforthisfunction):

Center5:

Equation:

Directions:Foreachwordproblembelowwriteanequation.Besuretoexplainyourthinkingasshownintheexampleabove.

Wordproblem

Thelocalbikeshopisrentingbikes.Torentabikeitcosts$5foraone-timefeeandthen$2anhour.

Equation:

c=2h+5 Totalcost

$2perhour Plus$5foraone-timefeemeaningnomatterhowmanyhoursIrentthebikeforIstillmustpaythe

$5.

Wordproblem

Sam’sclubishostingaspecialforValentine’sDay.Youcanbuya

membershipfortendollarsforayearwitha$3additionalfeeeachmonth.Howmuchwillyoupayaftereachmonth

throughoutanentireyear?-createatable

Wordproblem

Youhaveagumballmachinethathas500gumballsinit.Youhave2gumballseach

day.Writealinearequation.

Hint:youare“takingaway”gumballs

Center6:

::

Graphtoanequationy=(slope)(x)+(y-intercept)

y=1x+0ORy=x+0

TheslopegoesuponeoveronethereforeIwouldsubstituteapositive

oneintotheequationforslope

They-interceptisthepointwherethelinecrossesoverthey-axis.Herethelinecrossesoverthey–axisatzero.ThereforeIwould

substitutezeroinfory-intercept.

Iamthinkingthisonehasanegativeslopeoris

decreasingbecauseitisgoingdown.

Center7:

::

Createatableusingthegraphbelow.Use

atleast5pointstomakeyourtable

Vocabulary

Orderedpairs:Thexandyvalueofapointonacoordinategraph

PLOTTING

POINTS

Center8:

::

Center9:

::Discrete:Lookingatthenumberlinebelowdiscretefunctionscanonlybethenumbersseen;itcanNOTincludeany

numbersinbetweenthewholenumbers.

Ifyoulookabovethisdiscretefunctioncontainsonlythewholenumbers!

Continuous:Lookingatthenumberlinebelowdiscretefunctionscanonlybethenumbersseen;itcanNOTincludeanynumbersinbetweenthewholenumbers.

Ifyoulookabovethiscontinuousfunctioncontainsallthenumbersgreaterthan-5!

DiscreteverseContinuous:

Thisgraphisdiscretebecauseitonlyhasfourpointsonthegraphanditdoesnotincludethepointsinbetween.

ThisgraphiscontinuousbecauseitincludesALLthepointsontheline.

DiscreteverseContinuouscontinuedDiscreteExamples ContinuousExamples

The number of telephone calls received. The weight of a bag of apples.

The number of felony arrests in a town The length of a piece of wire

The number of telephone calls received is discrete because you cannot have ½ of a telephone call.

The weight of a bag of apples is continuous, because it can change in random intervals by adding or eliminating x

amount of apples at a time.

Decidewhetherthefollowingexamplesarediscreteorcontinuous.

Speed of a car Your weight before breakfast each morning

The length of hair growth over a one-month period A person's age

The amount of rainfall recorded each day for seven days The distance a golf ball travels after being hit with a driver

A local neighborhood community is asking everyone to participate in a new recycling program. At the end of each month, each house records the number of aluminum cans

they recycle.

The amount of rainfall in a year

The amount of money earned during an 8-hour workday The weight of newspapers collected at each house on a route

Pair’snumbersinthedomainwithnumbersin

therangeAnysetoforderedpairs

(x,y)

Mayormaynotbeafunction

Passestheverticallinetest

Arelationthatpairseachinputwithexactlyone

output

Atleastoneinputispairedwithmorethan

oneoutput

Tirepressure

Temperatureoutside

#ofcarsinaparkinglotsperhour

#ofstudentsatschooleachday

Aperson’sheight

ThenumberofcansofCokeonabeverage

deliverytruck

-8

-2

4

10

0

2

4

6

XY

-2

5

9

-2

1

3

7

5

XY

-2

3

5

4

0

1

3

1

XY

0

2

5

6

1

4

XY

-2

4

0

2

4

XY

Center10:

::Center10:

::

Cutouttheboxesabove.Gluethemunderthecorrectcategoriesincenter10.Thiswillbegradedtoseehowmuchyouhavelearned.Youmayuseyournotesand

yourpeersinyourgroupforhelp!

Relation

Function NotaFunction

Discrete Continuous

Iamamaster:

stampofapproval

Center10:

::