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数学专业英语系列课程函数专题I一、单词对照表坐标系1.直角坐标系orthogonalcoordinatesystem2.横轴abscissaaxis3.纵轴ordinateaxis4.横坐标abscissa5.纵坐标ordinate6.象限quadrant7.坐标coordinates8.距离distance函数的概念1.变量variable2.自变量independentvariable3.因变量dependentvariable4.函数function5.函数解析式analyticalfunctionexpression6.常量constant7.定义域domain8.函数值valueofafunction9.函数的图象thegraphofafunction一次函数1.正比例函数directproportionalfunction2.比例系数proportionalcoefficient3.一次函数linearfunction4.常函数constantfunction5.斜率slope6.截距(y轴上)y-intercrpt7.待定系数法methodofundeterminedcoefficient二、基本知识英汉互译在平面直角坐标系xOy中,点P所对应的的有序实数对ba,叫做点P的坐标,记作baP,,其中a叫做横坐标,b叫做纵坐标.IntherectangularcoordinatesystemxOy,thepairofrealnumbersba,correspondingtopointPiscalledthecoordinateofpointP,writtenasbaP,,aiscalledtheabscissa,andbiscalledtheordinate.请根据你所学的数学知识,将下列英语叙述的数学结论翻译成中文,部分词汇在单词对照表中未给出,请标出,可以在完成的过程中自己查询如果点yxC,在y轴上,则0x,y可以取一切实数.IfpointyxC,isontheordinateaxis,then0xandycouldbeanyrealnumber.垂直于纵轴的直线上的任意两点的坐标之间的关系是纵坐标相等.Theordinatesoftwopointsthatonastraightlineperpendiculartotheordinateaxismustbeequal.在直角坐标平面内,平行于x轴的直线上的两点01,yxA、02,yxB之间的距离为21xxAB,平行于y轴的直线上的两点10,yxC、20,yxD之间的距离为21yyCD.Intherectangularcoordinatesystem,thedistancebetweentwopoints01,yxA、02,yxBonthelineparalleltox-axisis21xxAB,thedistancebetweentwopoints10,yxC、20,yxDonthelineparalleltoy-axisis21yyCD.一般地,如果点yxM,沿着与x轴或y轴平行的方向平移0mm个单位,那么:向右平移后对应点的坐标为ymx,;向左平移后对应点的坐标为ymx,;向上平移后对应点的坐标为myx,;向下平移后对应点的坐标为myx,;Generally,ifpointyxM,translates0mmunitsinthedirectionofthex-axisorthey-axis,so:Movingtotheright,thecorrespondingcoordinateisymx,;Movingtotheleft,thecorrespondingcoordinateisymx,;Movingtothetop,thecorrespondingcoordinateismyx,;Movingtothebottom,thecorrespondingcoordinateismyx,;在问题研究中,可以取不同数值的量叫做变量,保持数值不变的量叫做常量.Avariableisavaluethatmaychangewithinthescopeofagivenproblemofsetofoperations.Incontrast,aconstantisavaluethatremainsunchanged,throughoftenunknownorundetermined.如果在某个变化过程中,有两个变量,设为x和y,变量y随着x的变化而变化,它们之间存在确定的依赖关系,那么变量y叫做变量x的函数,x叫做自变量yisafunctionofthevariablexwheneverdefinitevaluesofyareascribedtothevaluesofxbyacertainrule.xisanindependentvariableofthefunction.一般地,解析式形如bkxy(bk,是常数,且0k)的函数,叫做一次函数.一次函数的图象是一条直线.这条直线与y轴的交点坐标是b,0,纵坐标b叫做这条直线在y轴上的截距,简称直线的截距.Generally,afunctionoftheformbkxy,wherebk,areconstantsand0k,iscalledalinearfunction.Thegraphofanylinearfunctionisastraightline.Thelineandthey-axisintersectatpointb,0.They-interceptisthey-coordinstoofthepointwherethelinecrossesthey-axis.两直线平行:对于直线11bxky和直线22bxky,若21kk且21bb,则直线11bxky与直线22bxky平行;反之,如果两条直线直线11bxky和直线22bxky平行,那么,必有21kk且21bb.Forstraightline11bxkyandstraightline22bxky,if21kkand21bb,thenstraightline11bxkyisparalleltostraightline22bxky.Conversely,ifstraightline11bxkyisparalleltostraightline22bxky,then21kkand21bb.一般来说,一次函数bkxy(bk,是常数,且0k)具有以下性质:当0k时,y随x的增大而增大;当0k时,y随x的增大而减小.Generallyspeaking,thelinearfunctionbkxy,whenwherebk,areconstantsand0k,hasthefollowingproperty:when0k,yincreaseswhilexisincreasing;when0k,ydecreaseswhilexisincreasing.由于bk,的符号不同,直线bkxy所经过的象限也不同.当0,0bk时,直线经过第一、二、三象限;当0,0bk时,直线经过第一、三、四象限;当0,0bk时,直线经过第一、二、四象限;当0,0bk时,直线经过第二、三、四象限.Asbk,havedifferentsighs,thestraightlinebkxypassesdifferentquadrants.If0,0bk,thestraightlinepassesquadrantI,quadrantIIandquadrantIII;If0,0bk,thestraightlinepassesquadrantI,quadrantIIIandquadrantIV;If0,0bk,thestraightlinepassesquadrantI,quadrantIIandquadrantiv;If0,0bk,thestraightlinepassesquadrantII,quadrantIIIandquadrantIV.三、简单问题请你将下面几个简单的问题翻译成为中文,解决下面几个简单的问题,并用英语书写解答过程1.GivenpointaaP3,102isinquadrantIII.Findtherangeofa.2.Giventhatpoint73,1aaQisontheangularbisectorofquadrantIandquadrantIII,whatisa?3.Inarectangularcoordinateplane,drawastraightlinethroughpoints0,5Aand3,0B.Figureoutthefunctionofthestraightline.Whatistheareaofthetrianglemadeupbythestraightlineandtheaxises?4.Inarectangularcoordinateplane,alinearfunctionisdefinedbytheequation233xy.Thegraphofthefunctionintersectsx-axisatpointA,andintersectsy-axisatpointB.Givenpoint0,1C,PointDonx-axis,andABDBCD.FigureoutthefunctionofthestraightlinethroughpointsDB,.5.Asshowninthefigure,thegraphoflinearfunction133xyintersectsx-axisatpointA,intersectsy-axisatpointB.Given90BAC,point21,aPinquadrantII,ABCABPSS.Whatisa?
本文标题:数学专业英语一次函数专题
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