Name:______________________________________________________ Date:________________
MIF8Chapter6Section1
Mrs.Haywardplanstobringsomeofherstudentstoamuseum.Theadmissionfeeis
$7peradultand$3.50perstudent.Supposethatshebrings10students.Shewill
needtobuyticketsforoneadultandtenstudents.
Totaladmissionfee=_______________________________+_______________________________
=
=
=
TheadmissionfeeMrs.Haywardpaysispairedwiththenumberofstudentsshe
brings.Ifshebringsadifferentnumberofstudents,theadmissionfeewillbe
differentaswell.Thispairingoftwoquantitiesiscalleda___________________________and
canbeexpressedasanorderedpair.
Whenyouhavetwoquantities,oneistheindependentvariable,or__________________.
Thisquantitydeterminesthedependentvariable,or_______________________________.
Inthissituation,theindependentvariableis_________________________________________.
Thedependentvariableis______________________________________________________________.
Arelationis____________________________________________________________________________.
Arelationisafunctionifeveryinputhasexactlyoneoutput.
•
Thex-valuescannotberepeated
•
They-valuescanrepeat
Representingrelationsusingamappingdiagram
Onewaytorepresentarelationisinamappingdiagram.Let’ssaywehavethe
relationthatconsistsofthepoints 0, 0 , 0, 1 , 𝑎𝑛𝑑 1, 2 .
Input Relation
Output
Isthisafunction?_______________because______________________________________________
1.Thetableshowsthetestscoresoffivestudents.Useamappingdiagramtoshow
therelationbetweenthestudentsandtheirtestscores.Thenidentifythetypeof
relation.
Input (Student)
Relation
Output
(Testscores)
Isthisrelationafunction?
______________
because:
_______________________________
_______________________________
2.Iseachrelationshipafunction?Whyorwhynot?
_________________________________________
_______________________________________
3.Thetableshowstherelation
betweentheheightsoffivestatuesandtheir
weights.Useamappingdiagramtoshowthe
relationandidentifythetypeofrelation.
Input Relation
Output
______________ _______________ Height(in)
40
35
56
70
40
Weight(lb)
85
84
90
99
62
Isthisafunction?
_______________
because:
_______________________________
_______________________________
Tellingwhetherarelationisafunctionfromamappingdiagram
1.Thetableshowsthe
athletesthatcompetedin
thehighjumpatatrack
meet.
a.Writetherelationasalistoforderedpairs:
b.Completeamappingdiagramtoshowtherelation
_______________Relation_______________
c.Istherelationafunction?
d.Supposethedatawereswitchedandtheheightistheinputandtheathletenumber
istheoutput.Createamappingdiagramtodisplaythisrelation.
_______________Relation_______________
e.Istherelationafunction?
IdentifyingFunctionsGraphically
Anotherwaytodetermineifarelationisafunctionisby
usingagraph.Sinceeachinput(x-valueonagraph)can
onlybemappedontooneoutput(y-valueonagraph),we
canusetheverticallinetesttodetermineiftherelation
isafunction.
MappingDiagram Graph
Function?
Practice
1.Thegraphshowstherelationbetweenthe
heightseightstudentscanjumpintotheair,y
cm,andthestudents’heights,xcm.Tell
whethertherelationrepresentedbythegraph
isafunction.
2.Ifarocketislaunchedstraightupintheair,it
travelsquicklyatfirsttheslowsdownuntilit
beginstofallbacktowardtheground.The
graphshowsthedistance,hmeters,oftherocket
aftertsecondshavepassed.Istherelationa
function?
Circletherelationsthatarefunctions.Explainyourreasoningbeloweachgraph.