函数英文知识课件.pptx

FunctionEnglishPPTcourseware

contents目录DefinitionandpropertiesoffunctionsCommonfunctiontypesOperationandTransformationofFunctionsApplicationoffunctionsTheLimitandContinuityofFunctions

01Definitionandpropertiesoffunctions

Afunctionisafundamentalconceptinmathematics,whichisamappingrelationshipfromaninputsettoanoutputset.Thefunctiondefinitionusuallyincludesasetofinputvalues,anoutputvalueset,andacorrespondingrule,thatis,theinputvalueobtainstheoutputvaluethroughacertainoperationalrelationship.Definitionoffunctions

Thepropertiesoffunctionsincludedomain,range,monotonicity,parity,andsoon.Adomainisasetofinputvaluesforafunction,andavaluedomainisasetofoutputvaluesforafunction.Monotonicitydescribestheincreaseordecreaseofafunctionwithinacertaininterval,whileparitydescribeswhetherthefunctionissymmetricabouttheorigin.Thepropertiesoffunctions

Functionscanbeclassifiedaccordingtodifferentcriteria,suchaslinearfunctions,quadraticfunctions,trigonometricfunctions,etc.Functionscanalsobedividedintoopenfunctions,closedfunctions,semiopenandsemiclosedfunctionsbasedontherelationshipbetweentheirdomainofdefinitionandrangeofvalues.Inaddition,functionscanalsobedividedintodifferentiableandnondifferentiablefunctionsbasedonwhethertheyaredifferentiable.Classificationoffunctions

02Commonfunctiontypes

Linearfunctionisacommontypeoffunctioninmathematics,representedbyastraightline.Thegeneralformofalinearfunctionisy=ax+b,whereaandbareconstantsanda≠0.Thecharacteristicsoflinearfunctionsinclude:whena0,thefunctionisanincreasingfunction;Whena0,thefunctionisasubtractionfunction.Linearfunctionshaveawiderangeofapplicationsinreallife,suchaseconomics,statistics,andotherfields.Linearfunction

Quadraticfunctionisacommontypeofmathematicalfun