反比例函數(shù)典型例題以及知識點歸納

反比例函數(shù)典型例題以及知識點歸納反比例函數(shù)知識點歸納和典型例題知識點歸納,一,反比例函數(shù)的概念1,,,可以寫成,,的形式，注意自變量x的指數(shù)為，在解決有關(guān)自變量指數(shù)問題時應(yīng)特別注意系數(shù)這一限制條件,2,,,也可以寫成xy=k的形式，用它可以迅速地求出反比例函數(shù)解析式中的k，從而得到反比例函數(shù)的解析式,3,反比例函數(shù)的自變量，故函數(shù)圖象與x軸、y軸無交點,,二,反比例函數(shù)的圖象在用描點法畫反比例函數(shù)的圖象時，應(yīng)注意自變量x的取值不能為0，且x應(yīng)對稱取點,關(guān)于原點對稱,,,三,反比例函數(shù)及其圖象的性質(zhì)1,函數(shù)解析式:,,2,自變量的取值范圍:3,圖象:,1,圖象的形狀:雙曲線,越大，圖象的彎曲度越小，曲線越平直,越小，圖象的彎曲度越大,,2,圖象的位置和性質(zhì):與坐標(biāo)軸沒有交點，稱兩條坐標(biāo)軸是雙曲線的漸近線,當(dāng)時，圖象的兩支分別位于一、三象限,在每個象限內(nèi)，y隨x的增大而減小,當(dāng)時，圖象的兩支分別位于二、四象限,在每個象限內(nèi)，y隨x的增大而增大,,3,對稱性:圖象關(guān)于原點對稱，即若,a，b,在雙曲線的一支上，則,，,在雙曲線的另一支上,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圖象關(guān)于直線對稱，即若,a，b,在雙曲線的一支上，則,，,和,，,在雙曲線的另一支上,4,k的幾何意義如圖1，設(shè)點P,a，b,是雙曲線上任意一點，作PA?x軸于A點，PB?y軸于B點，則矩形PBOA的面積是,三角形PAO和三角形PBO的面積都是,,如圖2，由雙曲線的對稱性可知，P關(guān)于原點的對稱點Q也在雙曲線上，作QC?PA的延長線于C，則有三角形PQC的面積為,圖1圖25,說明:,1,雙曲線的兩個分支是斷開的，研究反比例函數(shù)的增減性時，要將兩個分支分別討論，不能一概而論,,2,直線與雙曲線的當(dāng)關(guān)系:時，兩圖象沒有交點,當(dāng)時，兩圖象必有兩個交點，且這兩個交點關(guān)于原點成中心對稱,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,充分利用數(shù)形結(jié)合的思想解決問題,例題分析1,反比例函數(shù)的概念,1,下列函數(shù)中，y是x的反比例函數(shù)的是,,,A,y=3xB,C,3xy=1D,,2,下列函數(shù)中，y是x的反比例函數(shù)的是,,,A,B,C,D,2,圖象和性質(zhì),1,已知函數(shù)是反比例函數(shù)，?若它的圖象在第二、四象限內(nèi)，那么k=_________?若y隨x的增大而減小，那么k=___________,,2,已知一次函數(shù)y=ax+b的圖象經(jīng)過第一、二、四象限，則函數(shù)的圖象位于第________象限,,3,若反比例函數(shù)經(jīng)過點,，2,，則一次函數(shù)的圖象一定不經(jīng)過第_____象限,,4,已知a?b，0，點P,a，b,在反比例函數(shù)的圖象上，則直線不經(jīng)過的象限是,,,A,第一象限B,第二象限C,第三象限D(zhuǎn),第四象限,5,若P,2，2,和Q,m，,是反比例函數(shù)圖象上的兩點，則一次函數(shù)y=kx+m的圖象經(jīng)過,,,A,第一、二、三象限B,第一、二、四象限C,第一、三、四象限D(zhuǎn),第二、三、四象限,6,已知函數(shù)和,k?0,，它們在同一坐標(biāo)系內(nèi)的圖象大致是,,,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,函數(shù)的增減性,1,在反比例函數(shù)的圖象上有兩點，，且，則的值為,,,A,正數(shù)B,負數(shù)C,非正數(shù)D,非負數(shù),2,在函數(shù),a為常數(shù),的圖象上有三個點，，，則函數(shù)值、、的大小關(guān)系是,,,A,，，B,，，C,，，D,，，,3,下列四個函數(shù)中:?,?,?,?,y隨x的增大而減小的函數(shù)有,,,A,0個B,1個C,2個D,3個,4,已知反比例函數(shù)的圖象與直線y=2x和y=x+1的圖象過同一點，則當(dāng)x，0時，這個反比例函數(shù)的函數(shù)值y隨x的增大而______,填“增大”或“減小”,,4,解析式的確定,1,若與成反比例，與成正比例，則y是z的,,,A,正比例函數(shù)B,反比例函數(shù)C,一次函數(shù)D,不能確定,2,若正比例函數(shù)y=2x與反比例函數(shù)的圖象有一個交點為,2，m,，則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=________，它們的另一個交點為________,,3,已知反比例函數(shù)的圖象經(jīng)過點，反比例函數(shù)的圖象在第二、四象限，求的值,,4,已知一次函數(shù)y=x+m與反比例函數(shù),,的圖象在第一象限內(nèi)的交點為P,x0，3,,?求x0的值,?求一次函數(shù)和反比例函數(shù)的解析式,5,面積計算,1,如圖，在函數(shù)的圖象上有三個點A、B、C，過這三個點分別向x軸、y軸作垂線，過每一點所作的兩條垂線段與x軸、y軸圍成的矩形的面積分別為、、，則,,,A,B,C,D,第,1,題圖第,2,題圖,2,如圖，A、B是函數(shù)的圖象上關(guān)于原點O對稱的任意兩點，AC//y軸，BC//x軸，?ABC的面積S，則,,,A,S=1B,1，S，2C,S=2D,S，2,3,如圖，Rt?AOB的頂點A在雙曲線上，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,題圖第,4,題圖,4,已知函數(shù)的圖象和兩條直線y=x，y=2x在第一象限內(nèi)分別相交于P1和P2兩點，過P1分別作x軸、y軸的垂線P1Q1，P1R1，垂足分別為Q1，R1，過P2分別作x軸、y軸的垂線P2Q2，P2R2，垂足分別為Q2，R2，求矩形OQ1P1R1和OQ2P2R2的周長，并比較它們的大小,,5,如圖，正比例函數(shù)y=kx,k，0,和反比例函數(shù)的圖象相交于A、C兩點，過A作x軸垂線交x軸于B，連接BC，若?ABC面積為S，則S=_________,第,5,題圖第,6,題圖,6,如圖在Rt?ABO中，頂點A是雙曲線與直線在第四象限的交點，AB?x軸于B且S?ABO=,?求這兩個函數(shù)的解析式,?求直線與雙曲線的兩個交點A、C的坐標(biāo)和?AOC的面積,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,如圖，已知正方形OABC的面積為9，點O為坐標(biāo)原點，點A、C分別在x軸、y軸上，點B在函數(shù),k，0，x，0,的圖象上，點P,m，n,是函數(shù),k，0，x，0,的圖象上任意一點，過P分別作x軸、y軸的垂線，垂足為E、F，設(shè)矩形OEPF在正方形OABC以外的部分的面積為S,?求B點坐標(biāo)和k的值,?當(dāng)時，求點P的坐標(biāo),?寫出S關(guān)于m的函數(shù)關(guān)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,綜合應(yīng)用,1,若函數(shù)y=k1x,k1?0,和函數(shù),k2?0,在同一坐標(biāo)系內(nèi)的圖象沒有公共點，則k1和k2,,,A,互為倒數(shù)B,符號相同C,絕對值相等D,符號相反,2,如圖，一次函數(shù)的圖象與反比例數(shù)的圖象交于A、B兩點:A,，1,，B,1，n,,?求反比例函數(shù)和一次函數(shù)的解析式,?根據(jù)圖象寫出使一次函數(shù)的值大于反比例函數(shù)的值的x的取值范圍,,3,如圖所示，已知一次函數(shù),k?0,的圖象與x軸、y軸分別交于A、B兩點，且與反比例函數(shù),m?0,的圖象在第一象限交于C點，CD垂直于x軸，垂足為D，若OA=OB=OD=1,?求點A、B、D的坐標(biāo),?求一次函數(shù)和反比例函數(shù)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-