反比例函数典型例题以及知识点归纳

反比例函数典型例题以及知识点归纳反比例函数知识点归纳和典型例题知识点归纳,一,反比例函数的概念1,,,可以写成,,的形式，注意自变量x的指数为，在解决有关自变量指数问题时应特别注意系数这一限制条件,2,,,也可以写成xy=k的形式，用它可以迅速地求出反比例函数解析式中的k，从而得到反比例函数的解析式,3,反比例函数的自变量，故函数图象与x轴、y轴无交点,,二,反比例函数的图象在用描点法画反比例函数的图象时，应注意自变量x的取值不能为0，且x应对称取点,关于原点对称,,,三,反比例函数及其图象的性质1,函数解析式:,,2,自变量的取值范围:3,图象:,1,图象的形状:双曲线,越大，图象的弯曲度越小，曲线越平直,越小，图象的弯曲度越大,,2,图象的位置和性质:与坐标轴没有交点，称两条坐标轴是双曲线的渐近线,当时，图象的两支分别位于一、三象限,在每个象限内，y随x的增大而减小,当时，图象的两支分别位于二、四象限,在每个象限内，y随x的增大而增大,,3,对称性:图象关于原点对称，即若,a，b,在双曲线的一支上，则,，,在双曲线的另一支上,designofurbanbridge(CJJ11-2011),Generalspecificationfordesignofhighwaybridgesandculverts(JTGD60-2004)codefordesignofreinforcedconcreteandprestressedconcreteHighway(JTGD62-2004)ofthehighwaybridgedesignspecificationsformasonry(JTGD61-2005)codefordesignofhighwaybridgeandculvert1,coursename:carairconditioningrepairMoZhen,Editor2,coursecode:3,credits/units:160hours4,major:automobilemaintenanceandtestingspecialtysecondnatureandtask1,course,course:thiscourseisaprofessionalcourseofautomobilemaintenanceandtestingspecialty.2,task:theteachingofthismoduleistotheautomotiveairconditioningrepairclassteachinginconjunctionwithtrainingcourses,small-classteachingandpracticaltrainingintheteachingprocess,theoryforsufficientdegree,withafocusonfosteringstudents'practicalskills.Throughthismodulestudentslearncanmastertheskillsofmaintenanceofautoairconditioning;theorywithpractice,testing,analysis,judgementandskilltohelptroubleshootautoairconditioningincommon,whichreflecttheautomobileapplicationtechnologySummaryofexcavationofFoundationpitengineeringbelowreferstothesurfaceofasupportingsystemofundergroundspaceanditssupporting.Toensure图象关于直线对称，即若,a，b,在双曲线的一支上，则,，,和,，,在双曲线的另一支上,4,k的几何意义如图1，设点P,a，b,是双曲线上任意一点，作PA?x轴于A点，PB?y轴于B点，则矩形PBOA的面积是,三角形PAO和三角形PBO的面积都是,,如图2，由双曲线的对称性可知，P关于原点的对称点Q也在双曲线上，作QC?PA的延长线于C，则有三角形PQC的面积为,图1图25,说明:,1,双曲线的两个分支是断开的，研究反比例函数的增减性时，要将两个分支分别讨论，不能一概而论,,2,直线与双曲线的当关系:时，两图象没有交点,当时，两图象必有两个交点，且这两个交点关于原点成中心对称,thiscourseisaprofessionalcourseofautomobilemaintenanceandtestingspecialty.2,task:theteachingofthismoduleisse:de:3,credits/units:160hours4,major:automobilemaintenanceandtestingspecialtysecondnatureandtask1,course,cour2005)codefordesignofhighwaybridgeandculvert1,coursename:carairconditioningrepairMoZhen,Editor2,courseco-12004)ofthehighwaybridgedesignspecificationsformasonry(JTGD6-2004)codefordesignofreinforcedconcreteandprestressedconcreteHighway(JTGD62-2011),Generalspecificationfordesignofhighwaybridgesandculverts(JTGD60-banbridge(CJJ11designofurtssupporting.ToensureandigySummaryofexcavationofFoundationpitengineeringbelowreferstothesurfaceofasupportingsystemofundergroundspace,judgementandskilltohelptroubleshootautoairconditioningincommon,whichreflecttheautomobileapplicationtechnoloalysishthismodulestudentslearncanmastertheskillsofmaintenanceofautoairconditioning;theorywithpractice,testing,antrainingintheteachingprocess,theoryforsufficientdegree,withafocusonfosteringstudents'practicalskills.Througclassteachingandpractical-totheautomotiveairconditioningrepairclassteachinginconjunctionwithtrainingcourses,small2,四,充分利用数形结合的思想解决问题,例题分析1,反比例函数的概念,1,下列函数中，y是x的反比例函数的是,,,A,y=3xB,C,3xy=1D,,2,下列函数中，y是x的反比例函数的是,,,A,B,C,D,2,图象和性质,1,已知函数是反比例函数，?若它的图象在第二、四象限内，那么k=_________?若y随x的增大而减小，那么k=___________,,2,已知一次函数y=ax+b的图象经过第一、二、四象限，则函数的图象位于第________象限,,3,若反比例函数经过点,，2,，则一次函数的图象一定不经过第_____象限,,4,已知a?b，0，点P,a，b,在反比例函数的图象上，则直线不经过的象限是,,,A,第一象限B,第二象限C,第三象限D,第四象限,5,若P,2，2,和Q,m，,是反比例函数图象上的两点，则一次函数y=kx+m的图象经过,,,A,第一、二、三象限B,第一、二、四象限C,第一、三、四象限D,第二、三、四象限,6,已知函数和,k?0,，它们在同一坐标系内的图象大致是,,,designofurbanbridge(CJJ11-2011),Generalspecificationfordesignofhighwaybridgesandculverts(JTGD60-2004)codefordesignofreinforcedconcreteandprestressedconcreteHighway(JTGD62-2004)ofthehighwaybridgedesignspecificationsformasonry(JTGD61-2005)codefordesignofhighwaybridgeandculvert1,coursename:carairconditioningrepairMoZhen,Editor2,coursecode:3,credits/units:160hours4,major:automobilemaintenanceandtestingspecialtysecondnatureandtask1,course,course:thiscourseisaprofessionalcourseofautomobilemaintenanceandtestingspecialty.2,task:theteachingofthismoduleistotheautomotiveairconditioningrepairclassteachinginconjunctionwithtrainingcourses,small-classteachingandpracticaltrainingintheteachingprocess,theoryforsufficientdegree,withafocusonfosteringstudents'practicalskills.Throughthismodulestudentslearncanmastertheskillsofmaintenanceofautoairconditioning;theorywithpractice,testing,analysis,judgementandskilltohelptroubleshootautoairconditioningincommon,whichreflecttheautomobileapplicationtechnologySummaryofexcavationofFoundationpitengineeringbelowreferstothesurfaceofasupportingsystemofundergroundspaceanditssupporting.Toensure3A,B,C,D,3,函数的增减性,1,在反比例函数的图象上有两点，，且，则的值为,,,A,正数B,负数C,非正数D,非负数,2,在函数,a为常数,的图象上有三个点，，，则函数值、、的大小关系是,,,A,，，B,，，C,，，D,，，,3,下列四个函数中:?,?,?,?,y随x的增大而减小的函数有,,,A,0个B,1个C,2个D,3个,4,已知反比例函数的图象与直线y=2x和y=x+1的图象过同一点，则当x，0时，这个反比例函数的函数值y随x的增大而______,填“增大”或“减小”,,4,解析式的确定,1,若与成反比例，与成正比例，则y是z的,,,A,正比例函数B,反比例函数C,一次函数D,不能确定,2,若正比例函数y=2x与反比例函数的图象有一个交点为,2，m,，则gySummaryofexcavationofFoundationpitengineeringbelowreferstothesurfaceofasupportingsystemofundergroundspace,judgementandskilltohelptroubleshootautoairconditioningincommon,whichreflecttheautomobileapplicationtechnoloalysishthismodulestudentslearncanmastertheskillsofmaintenanceofautoairconditioning;theorywithpractice,testing,antrainingintheteachingprocess,theoryforsufficientdegree,withafocusonfosteringstudents'practicalskills.Througclassteachingandpractical-totheautomotiveairconditioningrepairclassteachinginconjunctionwithtrainingcourses,smallthiscourseisaprofessionalcourseofautomobilemaintenanceandtestingspecialty.2,task:theteachingofthismoduleisse:de:3,credits/units:160hours4,major:automobilemaintenanceandtestingspecialtysecondnatureandtask1,course,cour2005)codefordesignofhighwaybridgeandculvert1,coursename:carairconditioningrepairMoZhen,Editor2,courseco-12004)ofthehighwaybridgedesignspecificationsformasonry(JTGD6-2004)codefordesignofreinforcedconcreteandprestressedconcreteHighway(JTGD62-2011),Generalspecificationfordesignofhighwaybridgesandculverts(JTGD60-banbridge(CJJ11designofurtssupporting.Toensureandi4m=_____，k=________，它们的另一个交点为________,,3,已知反比例函数的图象经过点，反比例函数的图象在第二、四象限，求的值,,4,已知一次函数y=x+m与反比例函数,,的图象在第一象限内的交点为P,x0，3,,?求x0的值,?求一次函数和反比例函数的解析式,5,面积计算,1,如图，在函数的图象上有三个点A、B、C，过这三个点分别向x轴、y轴作垂线，过每一点所作的两条垂线段与x轴、y轴围成的矩形的面积分别为、、，则,,,A,B,C,D,第,1,题图第,2,题图,2,如图，A、B是函数的图象上关于原点O对称的任意两点，AC//y轴，BC//x轴，?ABC的面积S，则,,,A,S=1B,1，S，2C,S=2D,S，2,3,如图，Rt?AOB的顶点A在双曲线上，且S?AOB=3，求m的值,designofurbanbridge(CJJ11-2011),Generalspecificationfordesignofhighwaybridgesandculverts(JTGD60-2004)codefordesignofreinforcedconcreteandprestressedconcreteHighway(JTGD62-2004)ofthehighwaybridgedesignspecificationsformasonry(JTGD61-2005)codefordesignofhighwaybridgeandculvert1,coursename:carairconditioningrepairMoZhen,Editor2,coursecode:3,credits/units:160hours4,major:automobilemaintenanceandtestingspecialtysecondnatureandtask1,course,course:thiscourseisaprofessionalcourseofautomobilemaintenanceandtestingspecialty.2,task:theteachingofthismoduleistotheautomotiveairconditioningrepairclassteachinginconjunctionwithtrainingcourses,small-classteachingandpracticaltrainingintheteachingprocess,theoryforsufficientdegree,withafocusonfosteringstudents'practicalskills.Throughthismodulestudentslearncanmastertheskillsofmaintenanceofautoairconditioning;theorywithpractice,testing,analysis,judgementandskilltohelptroubleshootautoairconditioningincommon,whichreflecttheautomobileapplicationtechnologySummaryofexcavationofFoundationpitengineeringbelowreferstothesurfaceofasupportingsystemofundergroundspaceanditssupporting.Toensure5第,3,题图第,4,题图,4,已知函数的图象和两条直线y=x，y=2x在第一象限内分别相交于P1和P2两点，过P1分别作x轴、y轴的垂线P1Q1，P1R1，垂足分别为Q1，R1，过P2分别作x轴、y轴的垂线P2Q2，P2R2，垂足分别为Q2，R2，求矩形OQ1P1R1和OQ2P2R2的周长，并比较它们的大小,,5,如图，正比例函数y=kx,k，0,和反比例函数的图象相交于A、C两点，过A作x轴垂线交x轴于B，连接BC，若?ABC面积为S，则S=_________,第,5,题图第,6,题图,6,如图在Rt?ABO中，顶点A是双曲线与直线在第四象限的交点，AB?x轴于B且S?ABO=,?求这两个函数的解析式,?求直线与双曲线的两个交点A、C的坐标和?AOC的面积,trainingintheteachingprocess,theoryforsufficientdegree,withafocusonfosteringstudents'practicalskills.Througclassteachingandpractical-totheautomotiveairconditioningrepairclassteachinginconjunctionwithtrainingcourses,smallthiscourseisaprofessionalcourseofautomobilemaintenanceandtestingspecialty.2,task:theteachingofthismoduleisse:de:3,credits/units:160hours4,major:automobilemaintenanceandtestingspecialtysecondnatureandtask1,course,cour2005)codefordesignofhighwaybridgeandculvert1,coursename:carairconditioningrepairMoZhen,Editor2,courseco-12004)ofthehighwaybridgedesignspecificationsformasonry(JTGD6-2004)codefordesignofreinforcedconcreteandprestressedconcreteHighway(JTGD62-2011),Generalspecificationfordesignofhighwaybridgesandculverts(JTGD60-banbridge(CJJ11designofurtssupporting.ToensureandigySummaryofexcavationofFoundationpitengineeringbelowreferstothesurfaceofasupportingsystemofundergroundspace,judgementandskilltohelptroubleshootautoairconditioningincommon,whichreflecttheautomobileapplicationtechnoloalysishthismodulestudentslearncanmastertheskillsofmaintenanceofautoairconditioning;theorywithpractice,testing,an6,7,如图，已知正方形OABC的面积为9，点O为坐标原点，点A、C分别在x轴、y轴上，点B在函数,k，0，x，0,的图象上，点P,m，n,是函数,k，0，x，0,的图象上任意一点，过P分别作x轴、y轴的垂线，垂足为E、F，设矩形OEPF在正方形OABC以外的部分的面积为S,?求B点坐标和k的值,?当时，求点P的坐标,?写出S关于m的函数关系式,designofurbanbridge(CJJ11-2011),Generalspecificationfordesignofhighwaybridgesandculverts(JTGD60-2004)codefordesignofreinforcedconcreteandprestressedconcreteHighway(JTGD62-2004)ofthehighwaybridgedesignspecificationsformasonry(JTGD61-2005)codefordesignofhighwaybridgeandculvert1,coursename:carairconditioningrepairMoZhen,Editor2,coursecode:3,credits/units:160hours4,major:automobilemaintenanceandtestingspecialtysecondnatureandtask1,course,course:thiscourseisaprofessionalcourseofautomobilemaintenanceandtestingspecialty.2,task:theteachingofthismoduleistotheautomotiveairconditioningrepairclassteachinginconjunctionwithtrainingcourses,small-classteachingandpracticaltrainingintheteachingprocess,theoryforsufficientdegree,withafocusonfosteringstudents'practicalskills.Throughthismodulestudentslearncanmastertheskillsofmaintenanceofautoairconditioning;theorywithpractice,testing,analysis,judgementandskilltohelptroubleshootautoairconditioningincommon,whichreflecttheautomobileapplicationtechnologySummaryofexcavationofFoundationpitengineeringbelowreferstothesurfaceofasupportingsystemofundergroundspaceanditssupporting.Toensure76,综合应用,1,若函数y=k1x,k1?0,和函数,k2?0,在同一坐标系内的图象没有公共点，则k1和k2,,,A,互为倒数B,符号相同C,绝对值相等D,符号相反,2,如图，一次函数的图象与反比例数的图象交于A、B两点:A,，1,，B,1，n,,?求反比例函数和一次函数的解析式,?根据图象写出使一次函数的值大于反比例函数的值的x的取值范围,,3,如图所示，已知一次函数,k?0,的图象与x轴、y轴分别交于A、B两点，且与反比例函数,m?0,的图象在第一象限交于C点，CD垂直于x轴，垂足为D，若OA=OB=OD=1,?求点A、B、D的坐标,?求一次函数和反比例函数的解析式,totheautomotiveairconditioningrepairclassteachinginconjunctionwithtrainingcourses,smallthiscourseisaprofessionalcourseofautomobilemaintenanceandtestingspecialty.2,task:theteachingofthismoduleisse:de:3,credits/units:160hours4,major:automobilemaintenanceandtestingspecialtysecondnatureandtask1,course,cour2005)codefordesignofhighwaybridgeandculvert1,coursename:carairconditioningrepairMoZhen,Editor2,courseco-12004)ofthehighwaybridgedesignspecificationsformasonry(JTGD6-2004)codefordesignofreinforcedconcreteandprestressedconcreteHighway(JTGD62-2011),Generalspecificationfordesignofhighwaybridgesandculverts(JTGD60-banbridge(CJJ11designofurtssupporting.ToensureandigySummaryofexcavationofFoundationpitengineeringbelowreferstothesurfaceofasupportingsystemofundergroundspace,judgementandskilltohelptroubleshootautoairconditioningincommon,whichreflecttheautomobileapplicationtechnoloalysishthismodulestudentslearncanmastertheskillsofmaintenanceofautoairconditioning;theorywithpractice,testing,antrainingintheteachingprocess,theoryforsufficientdegree,withafocusonfosteringstudents'practicalskills.Througclassteachingandpractical-