Linear Function Vocabularyjarrellmnps.weebly.com/.../6/3/3/86337132/linearfunctionsstationsca… ·...
Transcript of Linear Function Vocabularyjarrellmnps.weebly.com/.../6/3/3/86337132/linearfunctionsstationsca… ·...
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:
::