1_Functions.pdf

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Department
Mathematics
Course
MATA30H3
Professor
Sophie Chrysostomou
Semester
Fall

Description
FUNCTIONS11FUNCTIONSDEFINITIONAfunctionfwithdomainDisarulethatassociatestoeachelementxDasinglerealnumberyorfxThedomainoffisoftenwrittenasdomfAlsoxdomfisoftenexpressedasfisdenedatxofafunctionfisthesetofallofthefunctionvaluesTherangerangefyRyfxforsomexDWhenthefunctionisgivenbutitsdomainisnotmentionedweassumethedomainofthisfunctiontobethelargestsubsetofRforwhichthisfunctioncanbedened2xEXAMPLEfxc82013bySophieChrysostomou11FUNCTIONSTheVerticalLineTestThistestisusedtodetermineifarelationisafunctionArelationisafunctionifandonlyiftherearenoverticallinesthatintersectthegraphatmorethanonepointFunctionscanberepresentedbyanarrowdiagrambywordsbyatableofvaluesbyanalgebraicruleorbyagraphEXAMPLEofafunctionrepresentedbyagraph2525025ThusfhasdomainallthevaluesintheintervalandrangeallthevaluesintheintervalThesecanbereaddirectlyfromthegraphc92013bySophieChrysostomouFUNCTIONSDEFINITIONIffisafunctionfandfxfxforallxdomfthenfiscalledanevenfunctionIffxfxforallxdomfthenfiscalledanoddfunctionEXAMPLEDetermineifeachofthefollowingfunctionsisoddevenorneither24xx425ahx5xxbgxx5cfx3xxHOMEWORKShowthatitheproductoftwoevenfunctionsisanevenoneiitheproductoftwooddfunctionsisanevenoneiiitheproductofanoddandanevenfunctionisanoddonec102013bySophieChrysostomou
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