初二反比例函数

初二反比例数 反比例函数 1、知识梳理 ,1(1)反比例函数的定义:函数y,_____或y,kx(k是常数～k?0)叫做_______________; kk, 反比例函数y,中的是一个分式，所以自变量x?0，函数与x轴、y轴无交点( xx , 反比例函数解析式可以写成xy,k(k?0)，它明在反比例函数中自变量x与其对 应函数值y之积，总等于已知常数k. k(2)反比例函数的图象:反比例函数y,(k?0)的图象是__________; x 这两条曲线具有如下特征:?永不与x轴、y轴_______(因为x?0，k?0，相应地y值也不能为0，所以反比例函数的图象无限接近x轴和y轴);?是轴对称图形(对称轴是直线______或_____);?是中心对称图形(对称中心是点________); (3)反比例函数的性质: ?系数与位置间的关系: k,0?图象(双曲线)的两个分支分别在 _______象限内 k,0?图象(双曲线)的两个分支分别在 _______象限内 ?系数与函数的增减性: k,0?__________________(即函数为__________函数) k,0?__________________(即函数为__________函数) , 反比例函数的增减性与一次函数增减性不同:前者强调在_____________内，而后者则没有。这是一个易错点，避免出错的最好方法是____________法。 2、思路方法规律 k(1)反比例函数y,(k?0)中的k的几何意义 x k双曲线y,(k?0)上任意一点向两坐标轴作垂x 线，两垂线与坐标轴围成的矩形面积为|k|. S,k如图?和?，; 矩形PAOB design of urban bridge (CJJ 11-2011), General specification for design of highway bridges and culverts (JTG D60-2004) code for design of reinforced concrete and prestressed concrete Highway (JTG D62-2004) of the highway bridge design specifications for masonry (JTG D61-2005) code for design of highway bridge and culvert 1, course name: car air conditioning repair Mo Zhen, Editor 2, course code: 3, credits/units: 160 hours 4, major: automobile maintenance and testing specialty second nature and task 1, course, course: this course is a professional course of automobile maintenance and testing specialty. 2, task: the teaching of this module is to the automotive air conditioning repair class teaching in conjunction with training courses, small-class teaching and practical training in the teaching process, theory for sufficient degree, with a focus on fostering students ' practical skills. Through this module students learn can master the skills of maintenance of auto air conditioning; theory with practice, testing, analysis, judgement and skill to help troubleshoot auto air conditioning in common, which reflect the automobile application technologySummary of excavation of Foundation pit engineering below refers to the surface of a supporting system of underground space and its supporting. To ensure 11S,S,|xy|,|k|. ??OPAAOB22 (2)用待定系数法确定反比例函数的解析式 由于反比例函数的关系式中只有一个未知数，因此只需已知一组对应值就可以(待定系 数法求解析式的步骤: ?设出含有待定系数的函数解析式; ?把已知条件代入解析式，得到关于待定系数的方程; ?解方程求出待定系数( (3)反比例函数的应用 解决反比例函数的实际问时，先确定函数解析式，再利用图象找出解决问题的， 特别注意自变量的______________。 典例考题分析 3、 k题1:下列四个点中，有三个点在同一反比例函数y,的图象上，则不在这个函数图象上的((x 点是( ) 55A((5,1) B((,1,5) C((，3) D((,3，,) 33 k,1题2:反比例函数y,的图象在每条曲线上，y随x的增大而减小，则k的值可为( ) x A(,1 B(0 C(1 D(2 3:如图，在直角坐标系中，点A是x轴正半轴上的一个定点，点B是双曲线y,(x,题3x0)上的一个动点，当点B的横坐标逐渐增大时，?OAB的面积将会( ) A(逐渐增大 B(不变 C(逐渐减小 D(先增大后减小 1题4:已知反比例函数y,，下列结论不正确的是( ) (((x A(图象经过点(1,1) B(图象在第一、三象限 C(当x>1时，0y>y B(y>y>y C(y>y>y D(y>y>y 123132 312231 k,1题6:(1)已知反比例函数y,(k为常数，k?1)( x ?若点A(1,2)在这个函数的图象上，求k的值; design of urban bridge (CJJ 11-2011), General specification for design of highway bridges and culverts (JTG D60-2004) code for design of reinforced concrete and prestressed concrete Highway (JTG D62-2004) of the highway bridge design specifications for masonry (JTG D61-2005) code for design of highway bridge and culvert 1, course name: car air conditioning repair Mo Zhen, Editor 2, course code: 3, credits/units: 160 hours 4, major: automobile maintenance and testing specialty second nature and task 1, course, course: this course is a professional course of automobile maintenance and testing specialty. 2, task: the teaching of this module is to the automotive air conditioning repair class teaching in conjunction with training courses, small-class teaching and practical training in the teaching process, theory for sufficient degree, with a focus on fostering students ' practical skills. Through this module students learn can master the skills of maintenance of auto air conditioning; theory with practice, testing, analysis, judgement and skill to help troubleshoot auto air conditioning in common, which reflect the automobile application technologySummary of excavation of Foundation pit engineering below refers to the surface of a supporting system of underground space and its supporting. To ensure ?若在这个函数图象的每一支上，y随x的增大而减小，求k的取值范围; ?若k,13，试判断点B(3,4)，C(2,5)是否在这个函数的图象上，并说明理由( k(2)如图，已知反比例函数y,与一次函数y,x，b的图象在第一象x 限相交于点A(1，,k，4)( ?试确定这两个函数的表达式; ?求出这两个函数图象的另一个交点B的坐标，并根据图象写 出使反比例函数的值大于一次函数的值的x的取值范围( 4、考点训练 一、选择题 21(函数y,的图象经过的点是( ) x design of urban bridge (CJJ 11-2011), General specification for design of highway bridges and culverts (JTG D60-2004) code for 《反比例函数》第3页，共7页 design of reinforced concrete and prestressed concrete Highway (JTG D62-2004) of the highway bridge design specifications for masonry (JTG D61-2005) code for design of highway bridge and culvert 1, course name: car air conditioning repair Mo Zhen, Editor 2, course code: 3, credits/units: 160 hours 4, major: automobile maintenance and testing specialty second nature and task 1, course, course: this course is a professional course of automobile maintenance and testing specialty. 2, task: the teaching of this module is to the automotive air conditioning repair class teaching in conjunction with training courses, small-class teaching and practical training in the teaching process, theory for sufficient degree, with a focus on fostering students ' practical skills. Through this module students learn can master the skills of maintenance of auto air conditioning; theory with practice, testing, analysis, judgement and skill to help troubleshoot auto air conditioning in common, which reflect the automobile application technologySummary of excavation of Foundation pit engineering below refers to the surface of a supporting system of underground space and its supporting. To ensure 1A((2,1) B((2，,1) C((2,4) D((,，2) 2 2(如图所示的计算程序中，y与x之间的函数关系对应的图象所在的象限是( ) A(第一象限 B(第一、三象限 C(第二、四象限 D(第一、四象限 23(反比例函数y,(2m,1)xm,2，当x>0时，y随x的增大而增大，则m的值是( ) 1A(?1 B(小于的实数 C(,1 D(1 2 14(反比例函数y,,(x>0)的图象如图所示，随着x值的增大，yx 值( ) A(增大 B(减小 C(不变 D(先增大后减小 25的是( ) (已知反比例函数y,,，下列结论不正确(((x A(图象必经过点(,1,2) B(y随x的增大而增大 C(图象在第二、四象限内 D(若x>1，则,20)与双曲线y,交于A(x，y)、B(x，y)两点，1122x 则4xy,3xy,________. 1221 13(如图，A是反比例函数图象上一点，过点A作AB垂直y轴于点B，点P在x轴上，?ABP 的面积为2，则这个反比例函数的解析式为________( 414(函数y,x(x?0)，y,(x>0)的图象如图所示，则下列结论: 12x ?两函数图象的交点A的坐标为(2,2); ?当x>2时，y>y; 21 ?当x,1时，BC,3; ?当x逐渐增大时，y随着x的增大而增大，y随着x的增大而12减小( 其中正确的序号是________( 615(已知点A在双曲线y,上，且OA,4，过A作AC垂直x轴于x C，OA的垂直平分线交OC于B. design of urban bridge (CJJ 11-2011), General specification for design of highway bridges and culverts (JTG D60-2004) code for 《反比例函数》第5页，共7页 design of reinforced concrete and prestressed concrete Highway (JTG D62-2004) of the highway bridge design specifications for masonry (JTG D61-2005) code for design of highway bridge and culvert 1, course name: car air conditioning repair Mo Zhen, Editor 2, course code: 3, credits/units: 160 hours 4, major: automobile maintenance and testing specialty second nature and task 1, course, course: this course is a professional course of automobile maintenance and testing specialty. 2, task: the teaching of this module is to the automotive air conditioning repair class teaching in conjunction with training courses, small-class teaching and practical training in the teaching process, theory for sufficient degree, with a focus on fostering students ' practical skills. Through this module students learn can master the skills of maintenance of auto air conditioning; theory with practice, testing, analysis, judgement and skill to help troubleshoot auto air conditioning in common, which reflect the automobile application technologySummary of excavation of Foundation pit engineering below refers to the surface of a supporting system of underground space and its supporting. To ensure (1)?AOC的面积,______; (2)?ABC的周长为______( 三、解答题 16(如图，已知在平面直角坐标系xOy中，一次函数y,kx，b(k?0)的图象与反比例函数ym1,(m?0)的图象相交于A、B两点，且点B的纵坐标为,，过点A作AC垂直x轴于点x2 C，AC,1，OC,2. (1)求反比例函数的解析式; (2)求一次函数的解析式( 1k17(如图，正比例函数y,x的图象与反比例函数y,(k?0)在第一象限的图象交于A点，2x 过A点作x轴的垂线，垂足为M，已知?OAM的面积为1. (1)求反比例函数的解析式; (2)如果B为反比例函数在第一象限图象上的点(点B与点A不重合)，且B点的横坐标为1，在x轴上求一点P，使PA，PB最小( m18(如图，一次函数y,kx，2的图象与反比例函数y,的图象交于点P，点P在第一象限(PAx 垂直x轴于点A，PB垂直y轴于点B，一次函数的图象分别交x轴、y轴于点C、D，且S?PBD OC1,4，,. OA2 (1)求点D的坐标; (2)求一次函数与反比例函数的解析式; (3)根据图象写出当x>0时，一次函数的值大于反比例函数的值 design of urban bridge (CJJ 11-2011), General specification for design of highway bridges and culverts (JTG D60-2004) code for design of reinforced concrete and prestressed concrete Highway (JTG D62-2004) of the highway bridge design specifications for masonry (JTG D61-2005) code for design of highway bridge and culvert 1, course name: car air conditioning repair Mo Zhen, Editor 2, course code: 3, credits/units: 160 hours 4, major: automobile maintenance and testing specialty second nature and task 1, course, course: this course is a professional course of automobile maintenance and testing specialty. 2, task: the teaching of this module is to the automotive air conditioning repair class teaching in conjunction with training courses, small-class teaching and practical training in the teaching process, theory for sufficient degree, with a focus on fostering students ' practical skills. Through this module students learn can master the skills of maintenance of auto air conditioning; theory with practice, testing, analysis, judgement and skill to help troubleshoot auto air conditioning in common, which reflect the automobile application technologySummary of excavation of Foundation pit engineering below refers to the surface of a supporting system of underground space and its supporting. To ensure 的x的取值范围( kbky,19.如图，直线(,0)与双曲线(,0)在第一象限的一支相交于A、y,,x，bx B两点，与坐标轴交于C、D两点，P是双曲线上一点，且PO,PD。 ykb(1)试用、表示C、P两点的坐标; CA2)若?POD的面积等于1，试求双曲线在第一象限的一支的(y函数解析式; PxB43(3)在(2)的条件下，若?OAB的面积等于，试求?COA DxO 例2图 与?BOD的面积之和。 design of urban bridge (CJJ 11-2011), General specification for design of highway bridges and culverts (JTG D60-2004) code for 《反比例函数》第7页，共7页 design of reinforced concrete and prestressed concrete Highway (JTG D62-2004) of the highway bridge design specifications for masonry (JTG D61-2005) code for design of highway bridge and culvert 1, course name: car air conditioning repair Mo Zhen, Editor 2, course code: 3, credits/units: 160 hours 4, major: automobile maintenance and testing specialty second nature and task 1, course, course: this course is a professional course of automobile maintenance and testing specialty. 2, task: the teaching of this module is to the automotive air conditioning repair class teaching in conjunction with training courses, small-class teaching and practical training in the teaching process, theory for sufficient degree, with a focus on fostering students ' practical skills. Through this module students learn can master the skills of maintenance of auto air conditioning; theory with practice, testing, analysis, judgement and skill to help troubleshoot auto air conditioning in common, which reflect the automobile application technologySummary of excavation of Foundation pit engineering below refers to the surface of a supporting system of underground space and its supporting. To ensure