college algebra_concepts and contexts_0495387894_2010

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1、■LinearFunctionsAlinearfunctionisafunctionoftheformf1x2=b+mx.■Thegraphoffisalinewithslopemandy-interceptb.yybbxxÏ=bÏ=b+mx■ExponentialFunctionsxAnexponentialfunctionisafunctionoftheformf1x2=Ca.■Thegraphoffhasoneoftheshapesshown.■Ifa71,thenaiscalledthegrowthfactorandr=a-1iscalledthegr

2、owthrate.■If,a61thenaiscalledthedecayfactorandr=a-1iscalledthedecayrate.yy110x0xÏ=a˛,a>1Ï=a˛,0

3、loga=1logax=xalogax=xaaay01xÏ=logax,a>1■QuadraticFunctions2Aquadraticfunctionisafunctionoftheformf1x2=ax+bx+c.■Thegraphoffhastheshapeofaparabola.b■Themaximumorminimumvalueoffoccursatx=-.2a2■Thefunctionfcanbeexpressedinthestandardformf.1x2=a1x-h2+k■Thevertexofthegraphoffisatthepoint(

4、h,k).yy(h,k)0x(h,k)0xy=a(x-h)™+ky=a(x-h)™+ka<0,h>0,k>0a>0,h>0,k>0■PowerFunctionspApowerfunctionisafunctionoftheformf1x2=Cx.■Graphsofsomepowerfunctionsareshown.PositivepowersyyyyxxxxÏ=≈Ï=x£Ï=x¢Ï=x∞FractionalpowersyyyyxxxxÏ=œx∑Ï=œ£x∑Ï=œ¢x∑Ï=œ∞x∑Negativepowersyyyyxxxx1111Ï=xÏ=≈Ï=x£Ï=x¢

5、CollegeAlgebraCONCEPTSANDCONTEXTSABOUTTHEAUTHORSJAMESSTEWARTreceivedhisMSfromStanfordUniversityandhisPhDfromtheUniversityofToronto.HedidresearchattheUniversityofLondonandwasinfluencedbythefamousmathematicianGeorgePolyaatStanfordUniversity.StewartisProfessorEmeritusatMcMasterUniversi

6、tyandiscurrentlyProfessorofMathematicsattheUniversityofToronto.Hisresearchfieldisharmonicanalysisandtheconnectionsbetweenmathematicsandmusic.JamesStewartistheauthorofabestsellingcalculustextbookseriespublishedbyBrooks/Cole,CengageLearning,includingCalculus,Calculus:EarlyTranscendent

7、als,andCalculus:ConceptsandContexts;aseriesofprecalculustexts;andaseriesofhigh-schoolmathematicstextbooks.LOTHARREDLINgrewuponVancouverIsland,receivedaBachelorofSciencedegreefromtheUniversityofVictoria,andreceivedaPhDfromMcMasterUniversityin1978.Hesubsequentlydidresearchandtaughtatt

8、heUniversityofWashi