專題11反比例函數(shù)及其應(yīng)用（65題）一、單選題1．（2023·浙江·統(tǒng)考中考真題）如果SKIPIF1<0的壓力SKIPIF1<0作用于物體上，產(chǎn)生的壓強SKIPIF1<0要大于SKIPIF1<0，則下列關(guān)于物體受力面積SKIPIF1<0的說法正確的是（

）A．SKIPIF1<0小于SKIPIF1<0 B．SKIPIF1<0大于SKIPIF1<0 C．SKIPIF1<0小于SKIPIF1<0 D．SKIPIF1<0大于SKIPIF1<02．（2023·內(nèi)蒙古通遼·統(tǒng)考中考真題）已知點SKIPIF1<0在反比例函數(shù)SKIPIF1<0的圖像上，且SKIPIF1<0，則下列結(jié)論一定正確的是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2023·湖北宜昌·統(tǒng)考中考真題）某反比例函數(shù)圖象上四個點的坐標分別為SKIPIF1<0，則，SKIPIF1<0的大小關(guān)系為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2023·浙江嘉興·統(tǒng)考中考真題）已知點SKIPIF1<0均在反比例函數(shù)SKIPIF1<0的圖象上，則SKIPIF1<0的大小關(guān)系是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．（2023·云南·統(tǒng)考中考真題）若點SKIPIF1<0是反比例函數(shù)SKIPIF1<0圖象上一點，則常數(shù)SKIPIF1<0的值為（

）A．3 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．（2023·湖南永州·統(tǒng)考中考真題）已知點SKIPIF1<0在反比例函數(shù)SKIPIF1<0的圖象上，其中a，k為常數(shù)，且SKIPIF1<0﹐則點M一定在（

）A．第一象限 B．第二象限 C．第三象限 D．第四象限7．（2023·天津·統(tǒng)考中考真題）若點SKIPIF1<0都在反比例函數(shù)SKIPIF1<0的圖象上，則SKIPIF1<0的大小關(guān)系是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<08．（2023·湖北隨州·統(tǒng)考中考真題）已知蓄電池的電壓為定值，使用某蓄電池時，電流I(單位：A)與電阻R(單位：SKIPIF1<0)是反比例函數(shù)關(guān)系，它的圖象如圖所示，則當(dāng)電阻為SKIPIF1<0時，電流為(

)

A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<09．（2023·山西·統(tǒng)考中考真題）已知SKIPIF1<0都在反比例函數(shù)SKIPIF1<0的圖象上，則a、b、c的關(guān)系是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<010．（2023·吉林長春·統(tǒng)考中考真題）如圖，在平面直角坐標系中，點SKIPIF1<0、SKIPIF1<0在函數(shù)SKIPIF1<0的圖象上，分別以SKIPIF1<0、SKIPIF1<0為圓心，SKIPIF1<0為半徑作圓，當(dāng)SKIPIF1<0與SKIPIF1<0軸相切、SKIPIF1<0與SKIPIF1<0軸相切時，連結(jié)SKIPIF1<0，SKIPIF1<0，則SKIPIF1<0的值為（

）A．3 B．SKIPIF1<0 C．4 D．611．（2023·湖北·統(tǒng)考中考真題）在反比例函數(shù)SKIPIF1<0的圖象上有兩點SKIPIF1<0，當(dāng)SKIPIF1<0時，有SKIPIF1<0，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<012．（2023·湖南·統(tǒng)考中考真題）如圖，平面直角坐標系中，O是坐標原點，點A是反比例函數(shù)SKIPIF1<0圖像上的一點，過點A分別作SKIPIF1<0軸于點M，SKIPIF1<0軸于直N，若四邊形SKIPIF1<0的面積為2．則k的值是（

）

A．2 B．SKIPIF1<0 C．1 D．SKIPIF1<013．（2023·內(nèi)蒙古·統(tǒng)考中考真題）如圖，在平面直角坐標系中，SKIPIF1<0三個頂點的坐標分別為SKIPIF1<0與SKIPIF1<0關(guān)于直線SKIPIF1<0對稱，反比例函數(shù)SKIPIF1<0的圖象與SKIPIF1<0交于點SKIPIF1<0．若SKIPIF1<0，則SKIPIF1<0的值為（

）

A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<014．（2023·湖南懷化·統(tǒng)考中考真題）如圖，反比例函數(shù)SKIPIF1<0的圖象與過點SKIPIF1<0的直線SKIPIF1<0相交于SKIPIF1<0、SKIPIF1<0兩點．已知點SKIPIF1<0的坐標為SKIPIF1<0，點SKIPIF1<0為SKIPIF1<0軸上任意一點．如果SKIPIF1<0，那么點SKIPIF1<0的坐標為（

）

A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0或SKIPIF1<0 D．SKIPIF1<0或SKIPIF1<015．（2023·湖南·統(tǒng)考中考真題）如圖，矩形SKIPIF1<0的頂點SKIPIF1<0和正方形SKIPIF1<0的頂點SKIPIF1<0都在反比例函數(shù)SKIPIF1<0的圖像上，點SKIPIF1<0的坐標為SKIPIF1<0，則點SKIPIF1<0的坐標為（

）

A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<016．（2023·廣西·統(tǒng)考中考真題）如圖，過SKIPIF1<0的圖象上點A，分別作x軸，y軸的平行線交SKIPIF1<0的圖象于B，D兩點，以SKIPIF1<0，SKIPIF1<0為鄰邊的矩形SKIPIF1<0被坐標軸分割成四個小矩形，面積分別記為SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，若SKIPIF1<0，則SKIPIF1<0的值為（

）

A．4 B．3 C．2 D．117．（2023·福建·統(tǒng)考中考真題）如圖，正方形四個頂點分別位于兩個反比例函數(shù)SKIPIF1<0和SKIPIF1<0的圖象的四個分支上，則實數(shù)SKIPIF1<0的值為（）

A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．318．（2023·湖南張家界·統(tǒng)考中考真題）如圖，矩形SKIPIF1<0的頂點A，C分別在y軸、x軸的正半軸上，點D在SKIPIF1<0上，且SKIPIF1<0，反比例函數(shù)SKIPIF1<0的圖象經(jīng)過點D及矩形SKIPIF1<0的對稱中心M，連接SKIPIF1<0．若SKIPIF1<0的面積為3，則k的值為（

）

A．2 B．3 C．4 D．519．（2023·黑龍江·統(tǒng)考中考真題）如圖，SKIPIF1<0是等腰三角形，SKIPIF1<0過原點SKIPIF1<0，底邊SKIPIF1<0軸，雙曲線SKIPIF1<0過SKIPIF1<0兩點，過點SKIPIF1<0作SKIPIF1<0軸交雙曲線于點SKIPIF1<0，若SKIPIF1<0，則SKIPIF1<0的值是（

）

A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<020．（2023·黑龍江綏化·統(tǒng)考中考真題）在平面直角坐標系中，點A在y軸的正半軸上，SKIPIF1<0平行于x軸，點B，C的橫坐標都是3，SKIPIF1<0，點D在SKIPIF1<0上，且其橫坐標為1，若反比例函數(shù)SKIPIF1<0（SKIPIF1<0）的圖像經(jīng)過點B，D，則k的值是（

）A．1 B．2 C．3 D．SKIPIF1<021．（2023·四川宜賓·統(tǒng)考中考真題）如圖，在平面直角坐標系SKIPIF1<0中，點A、B分別在y，x軸上，SKIPIF1<0軸．點M、N分別在線段SKIPIF1<0、SKIPIF1<0上，SKIPIF1<0，SKIPIF1<0，反比例函數(shù)SKIPIF1<0的圖象經(jīng)過M、N兩點，P為x正半軸上一點，且SKIPIF1<0，SKIPIF1<0的面積為3，則k的值為（）

A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0二、填空題22．（2023·廣東·統(tǒng)考中考真題）某蓄電池的電壓為SKIPIF1<0，使用此蓄電池時，電流SKIPIF1<0(單位：SKIPIF1<0)與電阻SKIPIF1<0(單位：SKIPIF1<0)的函數(shù)表達式為SKIPIF1<0，當(dāng)SKIPIF1<0時，SKIPIF1<0的值為_______SKIPIF1<0．23．（2023·四川成都·統(tǒng)考中考真題）若點SKIPIF1<0都在反比例函數(shù)SKIPIF1<0的圖象上，則SKIPIF1<0_______SKIPIF1<0（填“SKIPIF1<0”或“SKIPIF1<0”）．24．（2023·浙江溫州·統(tǒng)考中考真題）在溫度不變的條件下，通過一次又一次地對汽缸頂部的活塞加壓，加壓后氣體對汽缸壁所產(chǎn)生的壓強P（SKIPIF1<0）與汽缸內(nèi)氣體的體積V（SKIPIF1<0）成反比例，P關(guān)于V的函數(shù)圖象如圖所示．若壓強由SKIPIF1<0加壓到SKIPIF1<0，則氣體體積壓縮了___________SKIPIF1<0．

25．（2023·河北·統(tǒng)考中考真題）如圖，已知點SKIPIF1<0，反比例函數(shù)SKIPIF1<0圖像的一支與線段SKIPIF1<0有交點，寫出一個符合條件的k的數(shù)值：_________．

26．（2023·湖北鄂州·統(tǒng)考中考真題）如圖，在平面直角坐標系中，直線SKIPIF1<0與雙曲線SKIPIF1<0（其中SKIPIF1<0）相交于SKIPIF1<0，SKIPIF1<0兩點，過點B作SKIPIF1<0軸，交y軸于點P，則SKIPIF1<0的面積是___________．

27．（2023·新疆·統(tǒng)考中考真題）如圖，在平面直角坐標系中，SKIPIF1<0為直角三角形，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0．若反比例函數(shù)SKIPIF1<0的圖象經(jīng)過SKIPIF1<0的中點SKIPIF1<0，交SKIPIF1<0于點SKIPIF1<0，則SKIPIF1<0______．

28．（2023·浙江紹興·統(tǒng)考中考真題）如圖，在平面直角坐標系SKIPIF1<0中，函數(shù)SKIPIF1<0（SKIPIF1<0為大于0的常數(shù)，SKIPIF1<0）圖象上的兩點SKIPIF1<0，滿足SKIPIF1<0．SKIPIF1<0的邊SKIPIF1<0軸，邊SKIPIF1<0軸，若SKIPIF1<0的面積為6，則SKIPIF1<0的面積是________．29．（2023·山東煙臺·統(tǒng)考中考真題）如圖，在直角坐標系中，SKIPIF1<0與SKIPIF1<0軸相切于點SKIPIF1<0為SKIPIF1<0的直徑，點SKIPIF1<0在函數(shù)SKIPIF1<0的圖象上，SKIPIF1<0為SKIPIF1<0軸上一點，SKIPIF1<0的面積為6，則SKIPIF1<0的值為________．

30．（2023·山東棗莊·統(tǒng)考中考真題）如圖，在反比例函數(shù)SKIPIF1<0的圖象上有SKIPIF1<0等點，它們的橫坐標依次為1，2，3，…，2024，分別過這些點作x軸與y軸的垂線，圖中所構(gòu)成的陰影部分的面積從左到右依次為SKIPIF1<0，則SKIPIF1<0___________．

31．（2023·四川內(nèi)江·統(tǒng)考中考真題）如圖，在平面直角坐標系中，O為坐標原點，SKIPIF1<0垂直于x軸，以SKIPIF1<0為對稱軸作SKIPIF1<0的軸對稱圖形，對稱軸SKIPIF1<0與線段SKIPIF1<0相交于點F，點D的對應(yīng)點B恰好落在反比例函數(shù)SKIPIF1<0的圖象上，點O、E的對應(yīng)點分別是點C、A．若點A為SKIPIF1<0的中點，且SKIPIF1<0，則k的值為___________．

32．（2023·黑龍江齊齊哈爾·統(tǒng)考中考真題）如圖，點A在反比例函數(shù)SKIPIF1<0圖像的一支上，點B在反比例函數(shù)SKIPIF1<0圖像的一支上，點C，D在x軸上，若四邊形SKIPIF1<0是面積為9的正方形，則實數(shù)k的值為______．

33．（2023·廣東深圳·統(tǒng)考中考真題）如圖，SKIPIF1<0與SKIPIF1<0位于平面直角坐標系中，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，若SKIPIF1<0，反比例函數(shù)SKIPIF1<0恰好經(jīng)過點C，則SKIPIF1<0______．34．（2023·江蘇連云港·統(tǒng)考中考真題）如圖，矩形SKIPIF1<0的頂點SKIPIF1<0在反比例函數(shù)SKIPIF1<0的圖像上，頂點SKIPIF1<0在第一象限，對角線SKIPIF1<0軸，交SKIPIF1<0軸于點SKIPIF1<0．若矩形SKIPIF1<0的面積是6，SKIPIF1<0，則SKIPIF1<0__________．

35．（2023·浙江寧波·統(tǒng)考中考真題）如圖，點A，B分別在函數(shù)SKIPIF1<0圖象的兩支上（A在第一象限），連接AB交x軸于點C．點D，E在函數(shù)SKIPIF1<0圖象上，SKIPIF1<0軸，SKIPIF1<0軸，連接SKIPIF1<0．若SKIPIF1<0，SKIPIF1<0的面積為9，四邊形SKIPIF1<0的面積為14，則SKIPIF1<0的值為__________，a的值為__________．

36．（2023·湖北荊州·統(tǒng)考中考真題）如圖，點SKIPIF1<0在雙曲線SKIPIF1<0上，將直線SKIPIF1<0向上平移若干個單位長度交SKIPIF1<0軸于點SKIPIF1<0，交雙曲線于點SKIPIF1<0．若SKIPIF1<0，則點SKIPIF1<0的坐標是___________．

三、解答題37．（2023·浙江杭州·統(tǒng)考中考真題）在直角坐標系中，已知SKIPIF1<0，設(shè)函數(shù)SKIPIF1<0與函數(shù)SKIPIF1<0的圖象交于點SKIPIF1<0和點SKIPIF1<0．已知點SKIPIF1<0的橫坐標是2，點SKIPIF1<0的縱坐標是SKIPIF1<0．

(1)求SKIPIF1<0的值．(2)過點SKIPIF1<0作SKIPIF1<0軸的垂線，過點SKIPIF1<0作SKIPIF1<0軸的垂線，在第二象限交于點SKIPIF1<0；過點SKIPIF1<0作SKIPIF1<0軸的垂線，過點SKIPIF1<0作SKIPIF1<0軸的垂線，在第四象限交于點SKIPIF1<0．求證：直線SKIPIF1<0經(jīng)過原點．38．（2023·湖南常德·統(tǒng)考中考真題）如圖所示，一次函數(shù)SKIPIF1<0與反比例函數(shù)SKIPIF1<0相交于點A和點SKIPIF1<0．

(1)求m的值和反比例函數(shù)解析式；(2)當(dāng)SKIPIF1<0時，求x的取值范圍．39．（2023·湖南·統(tǒng)考中考真題）如圖，點A的坐標是SKIPIF1<0，點B的坐標是SKIPIF1<0，點C為SKIPIF1<0中點，將SKIPIF1<0繞著點B逆時針旋轉(zhuǎn)SKIPIF1<0得到SKIPIF1<0．

(1)反比例函數(shù)SKIPIF1<0的圖像經(jīng)過點SKIPIF1<0，求該反比例函數(shù)的表達式；(2)一次函數(shù)圖像經(jīng)過A、SKIPIF1<0兩點，求該一次函數(shù)的表達式．40．（2023·四川自貢·統(tǒng)考中考真題）如圖，點SKIPIF1<0在反比例函數(shù)SKIPIF1<0圖象上．一次函數(shù)SKIPIF1<0的圖象經(jīng)過點A，分別交x軸，y軸于點B，C，且SKIPIF1<0與SKIPIF1<0的面積比為SKIPIF1<0．

(1)求反比例函數(shù)和一次函數(shù)的解析式；(2)請直接寫出SKIPIF1<0時，x的取值范圍．41．（2023·四川瀘州·統(tǒng)考中考真題）如圖，在平面直角坐標系SKIPIF1<0中，直線SKIPIF1<0與SKIPIF1<0，SKIPIF1<0軸分別相交于點A，B，與反比例函數(shù)SKIPIF1<0的圖象相交于點C，已知SKIPIF1<0，點C的橫坐標為2．(1)求SKIPIF1<0，SKIPIF1<0的值；(2)平行于SKIPIF1<0軸的動直線與SKIPIF1<0和反比例函數(shù)的圖象分別交于點D，E，若以B，D，E，O為頂點的四邊形為平行四邊形，求點D的坐標．42．（2023·四川南充·統(tǒng)考中考真題）如圖，一次函數(shù)圖象與反比例函數(shù)圖象交于點SKIPIF1<0，SKIPIF1<0，與x軸交于點C，與y軸交于點D．(1)求反比例函數(shù)與一次函數(shù)的解析式；(2)點M在x軸上，若SKIPIF1<0，求點M的坐標．43．（2023·四川宜賓·統(tǒng)考中考真題）如圖，在平面直角坐標系SKIPIF1<0中，等腰直角三角形SKIPIF1<0的直角頂點SKIPIF1<0，頂點A、SKIPIF1<0恰好落在反比例函數(shù)SKIPIF1<0第一象限的圖象上．

(1)分別求反比例函數(shù)的表達式和直線SKIPIF1<0所對應(yīng)的一次函數(shù)的表達式；(2)在x軸上是否存在一點P，使SKIPIF1<0周長的值最?。舸嬖冢蟪鲎钚≈担蝗舨淮嬖?，請說明理由．44．（2023·四川廣安·統(tǒng)考中考真題）如圖，一次函數(shù)SKIPIF1<0（SKIPIF1<0為常數(shù)，SKIPIF1<0）的圖象與反比例函數(shù)SKIPIF1<0為常數(shù)，SKIPIF1<0的圖象在第一象限交于點SKIPIF1<0，與SKIPIF1<0軸交于點SKIPIF1<0．

(1)求一次函數(shù)和反比例函數(shù)的解析式．(2)點SKIPIF1<0在SKIPIF1<0軸上，SKIPIF1<0是以SKIPIF1<0為腰的等腰三角形，請直接寫出點SKIPIF1<0的坐標．45．（2023·四川遂寧·統(tǒng)考中考真題）如圖，一次函數(shù)SKIPIF1<0的圖像與反比例函數(shù)SKIPIF1<0的圖像交于SKIPIF1<0，SKIPIF1<0兩點．（SKIPIF1<0，SKIPIF1<0，SKIPIF1<0為常數(shù)）

(1)求一次函數(shù)和反比例函數(shù)的解析式；(2)根據(jù)圖像直接寫出不等式SKIPIF1<0的解集；(3)SKIPIF1<0為SKIPIF1<0軸上一點，若SKIPIF1<0的面積為SKIPIF1<0，求SKIPIF1<0點的坐標．46．（2023·四川眉山·統(tǒng)考中考真題）如圖，在平面直角坐標系SKIPIF1<0中，直線SKIPIF1<0與x軸交于點SKIPIF1<0，與y軸交于點SKIPIF1<0，與反比例函數(shù)SKIPIF1<0在第四象限內(nèi)的圖象交于點SKIPIF1<0．

(1)求反比例函數(shù)的表達式：(2)當(dāng)SKIPIF1<0時，直接寫出x的取值范圍；(3)在雙曲線SKIPIF1<0上是否存在點P，使SKIPIF1<0是以點A為直角頂點的直角三角形？若存在，求出點P的坐標；若不存在，請說明理由．47．（2023·江西·統(tǒng)考中考真題）如圖，已知直線SKIPIF1<0與反比例函數(shù)SKIPIF1<0的圖象交于點SKIPIF1<0，與y軸交于點B，過點B作x軸的平行線交反比例函數(shù)SKIPIF1<0的圖象于點C．

(1)求直線SKIPIF1<0和反比例函數(shù)圖象的表達式；(2)求SKIPIF1<0的面積．48．（2023·四川樂山·統(tǒng)考中考真題）如圖，一次函數(shù)SKIPIF1<0的圖象與反比例函數(shù)SKIPIF1<0的圖象交于點SKIPIF1<0，與x軸交于點B，與y軸交于點SKIPIF1<0．

(1)求m的值和一次函數(shù)的表達式；(2)已知P為反比例函數(shù)SKIPIF1<0圖象上的一點，SKIPIF1<0，求點P的坐標．49．（2023·湖南岳陽·統(tǒng)考中考真題）如圖，反比例函數(shù)SKIPIF1<0（SKIPIF1<0為常數(shù)，SKIPIF1<0）與正比例函數(shù)SKIPIF1<0（SKIPIF1<0為常數(shù)，SKIPIF1<0）的圖像交于SKIPIF1<0兩點．

(1)求反比例函數(shù)和正比例函數(shù)的表達式；(2)若y軸上有一點SKIPIF1<0的面積為4，求點SKIPIF1<0的坐標．50．（2023·湖南·統(tǒng)考中考真題）如圖，正比例函數(shù)SKIPIF1<0的圖象與反比例函數(shù)SKIPIF1<0的圖象相交于點A．

(1)求點A的坐標．(2)分別以點O、A為圓心，大于SKIPIF1<0一半的長為半徑作圓弧，兩弧相交于點B和點C，作直線SKIPIF1<0，交x軸于點D．求線段SKIPIF1<0的長．51．（2023·江蘇蘇州·統(tǒng)考中考真題）如圖，一次函數(shù)SKIPIF1<0的圖象與反比例函數(shù)SKIPIF1<0的圖象交于點SKIPIF1<0．將點SKIPIF1<0沿SKIPIF1<0軸正方向平移SKIPIF1<0個單位長度得到點SKIPIF1<0為SKIPIF1<0軸正半軸上的點，點SKIPIF1<0的橫坐標大于點SKIPIF1<0的橫坐標，連接SKIPIF1<0的中點SKIPIF1<0在反比例函數(shù)SKIPIF1<0的圖象上．

(1)求SKIPIF1<0的值；(2)當(dāng)SKIPIF1<0為何值時，SKIPIF1<0的值最大?最大值是多少?52．（2023·山東東營·統(tǒng)考中考真題）如圖，在平面直角坐標系中，一次函數(shù)SKIPIF1<0與反比例函數(shù)SKIPIF1<0交于SKIPIF1<0，SKIPIF1<0兩點，與y軸交于點C，連接SKIPIF1<0，SKIPIF1<0．

(1)求反比例函數(shù)和一次函數(shù)的表達式；(2)求SKIPIF1<0的面積；(3)請根據(jù)圖象直接寫出不等式SKIPIF1<0的解集．53．（2023·山東棗莊·統(tǒng)考中考真題）如圖，一次函數(shù)SKIPIF1<0的圖象與反比例函數(shù)SKIPIF1<0的圖象交于SKIPIF1<0兩點．

(1)求一次函數(shù)的表達式，并在所給的平面直角坐標系中畫出這個一次函數(shù)的圖象；(2)觀察圖象，直接寫出不等式SKIPIF1<0的解集；(3)設(shè)直線SKIPIF1<0與x軸交于點C，若SKIPIF1<0為y軸上的一動點，連接SKIPIF1<0，當(dāng)SKIPIF1<0的面積為SKIPIF1<0時，求點P的坐標．54．（2023·山東濱州·統(tǒng)考中考真題）如圖，直線SKIPIF1<0為常數(shù)SKIPIF1<0與雙曲線SKIPIF1<0（SKIPIF1<0為常數(shù)）相交于SKIPIF1<0，SKIPIF1<0兩點．

(1)求直線SKIPIF1<0的解析式；(2)在雙曲線SKIPIF1<0上任取兩點SKIPIF1<0和SKIPIF1<0，若SKIPIF1<0，試確定SKIPIF1<0和SKIPIF1<0的大小關(guān)系，并寫出判斷過程；(3)請直接寫出關(guān)于SKIPIF1<0的不等式SKIPIF1<0的解集．55．（2023·四川內(nèi)江·統(tǒng)考中考真題）如圖，在平面直角坐標系中，一次函數(shù)SKIPIF1<0與反比例函數(shù)SKIPIF1<0的圖象在第一象限內(nèi)交于SKIPIF1<0和SKIPIF1<0兩點，直線SKIPIF1<0與x軸相交于點C，連接SKIPIF1<0．

(1)求一次函數(shù)與反比例函數(shù)的表達式；(2)當(dāng)SKIPIF1<0時，請結(jié)合函數(shù)圖象，直接寫出關(guān)于x的不等式SKIPIF1<0的解集；(3)過點B作SKIPIF1<0平行于x軸，交SKIPIF1<0于點D，求梯形SKIPIF1<0的面積．56．（2023·湖南·統(tǒng)考中考真題）如圖所示，在平面直角坐標系SKIPIF1<0中，四邊形SKIPIF1<0為正方形，其中點A、C分別在x軸負半軸，y軸負半軸上，點B在第三象限內(nèi)，點SKIPIF1<0，點SKIPIF1<0在函數(shù)SKIPIF1<0的圖像上

(1)求k的值；(2)連接SKIPIF1<0，記SKIPIF1<0的面積為S，設(shè)SKIPIF1<0，求T的最大值．57．（2023·湖北十堰·統(tǒng)考中考真題）函數(shù)SKIPIF1<0的圖象可以由函數(shù)SKIPIF1<0的圖象左右平移得到．(1)將函數(shù)SKIPIF1<0的圖象向右平移4個單位得到函數(shù)SKIPIF1<0的圖象，則SKIPIF1<0____；(2)下列關(guān)于函數(shù)SKIPIF1<0的性質(zhì)：①圖象關(guān)于點SKIPIF1<0對稱；②SKIPIF1<0隨SKIPIF1<0的增大而減??；③圖象關(guān)于直線SKIPIF1<0對稱；④SKIPIF1<0的取值范圍為SKIPIF1<0．其中說法正確的是________（填寫序號）；(3)根據(jù)（1）中SKIPIF1<0的值，寫出不等式SKIPIF1<0的解集：_________．58．（2023·甘肅蘭州·統(tǒng)考中考真題）如圖，反比例函數(shù)SKIPIF1<0與一次函數(shù)SKIPIF1<0的圖象交于點SKIPIF1<0，SKIPIF1<0軸于點D，分別交反比例函數(shù)與一次函數(shù)的圖象于點B，C．

(1)求反比例函數(shù)SKIPIF1<0與一次函數(shù)SKIPIF1<0的表達式；(2)當(dāng)SKIPIF1<0時，求線段SKIPIF1<0的長．59．（2023·湖北黃岡·統(tǒng)考中考真題）如圖，一次函數(shù)SKIPIF1<0與函數(shù)為SKIPIF1<0的圖象交于SKIPIF1<0兩點．

(1)求這兩個函數(shù)的解析式；(2)根據(jù)圖象，直接寫出滿足SKIPIF1<0時x的取值范圍；(3)點P在線段SKIPIF1<0上，過點P作x軸的垂線，垂足為M，交函數(shù)SKIPIF1<0的圖象于點Q，若SKIPIF1<0面積為3，求點P的坐標．60．（2023·四川·統(tǒng)考中