五年(19-23)中考數(shù)學(xué)真題與模擬卷分項(xiàng)匯編專題09 一次函數(shù)與反比例函數(shù)（原卷版）

專題09一次函數(shù)與反比例函數(shù)考點(diǎn)1一次函數(shù)與反比例函數(shù)一、單選題1．（2023年重慶市中考數(shù)學(xué)真題（B卷））反比例函數(shù)SKIPIF1<0的圖象一定經(jīng)過的點(diǎn)是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2023年湖南省湘潭市中考數(shù)學(xué)真題）如圖，平面直角坐標(biāo)系中，O是坐標(biāo)原點(diǎn)，點(diǎn)A是反比例函數(shù)SKIPIF1<0圖像上的一點(diǎn)，過點(diǎn)A分別作SKIPIF1<0軸于點(diǎn)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<03．（2023年湖南省長沙市中考數(shù)學(xué)真題）下列一次函數(shù)中，y隨x的增大而減小的函數(shù)是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2020·廣西賀州·統(tǒng)考中考真題）在反比例函數(shù)SKIPIF1<0中，當(dāng)SKIPIF1<0時(shí)，y的值為（

）A．2 B．SKIPIF1<0 C．SKIPIF1<0? D．SKIPIF1<05．（2020·四川巴中·統(tǒng)考中考真題）如圖，一次函數(shù)y1＝ax+b（a≠0）與反比例函數(shù)SKIPIF1<0（k≠0，x＞0）的交點(diǎn)A坐標(biāo)為（2，1），當(dāng)y1≤y2時(shí)，x的取值范圍是（）A．0＜x≤2 B．0＜x＜2 C．x＞2 D．x≥26．（2021·貴州黔西·中考真題）對(duì)于反比例函數(shù)y＝﹣SKIPIF1<0，下列說法錯(cuò)誤的是（）A．圖象經(jīng)過點(diǎn)（1，﹣5）B．圖象位于第二、第四象限C．當(dāng)x＜0時(shí)，y隨x的增大而減小D．當(dāng)x＞0時(shí)，y隨x的增大而增大7．（2022·湖南懷化·統(tǒng)考中考真題）如圖，直線AB交x軸于點(diǎn)C，交反比例函數(shù)y＝SKIPIF1<0（a＞1）的圖像于A、B兩點(diǎn)，過點(diǎn)B作BD⊥y軸，垂足為點(diǎn)D，若S△BCD＝5，則a的值為（）A．8 B．9 C．10 D．118．（2022·山東濱州·統(tǒng)考中考真題）在同一平面直角坐標(biāo)系中，函數(shù)SKIPIF1<0與SKIPIF1<0（k為常數(shù)且SKIPIF1<0）的圖象大致是（

）A． B．C． D．9．（2023年甘肅省蘭州市中考數(shù)學(xué)真題）一次函數(shù)SKIPIF1<0的函數(shù)值y隨x的增大而減小，當(dāng)SKIPIF1<0時(shí)，y的值可以是（

）A．2 B．1 C．－1 D．－210．（2023年湖南省邵陽市中考數(shù)學(xué)真題）如圖，矩形SKIPIF1<0的頂點(diǎn)SKIPIF1<0和正方形SKIPIF1<0的頂點(diǎn)SKIPIF1<0都在反比例函數(shù)SKIPIF1<0的圖像上，點(diǎn)SKIPIF1<0的坐標(biāo)為SKIPIF1<0，則點(diǎn)SKIPIF1<0的坐標(biāo)為（

）

A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<011．（2023年廣西壯族自治區(qū)中考數(shù)學(xué)真題）如圖，過SKIPIF1<0的圖象上點(diǎn)A，分別作x軸，y軸的平行線交SKIPIF1<0的圖象于B，D兩點(diǎn)，以SKIPIF1<0，SKIPIF1<0為鄰邊的矩形SKIPIF1<0被坐標(biāo)軸分割成四個(gè)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．112．（2019·四川眉山·統(tǒng)考中考真題）如圖，一束光線從點(diǎn)SKIPIF1<0出發(fā)，經(jīng)SKIPIF1<0軸上的點(diǎn)SKIPIF1<0反射后經(jīng)過點(diǎn)SKIPIF1<0，則點(diǎn)SKIPIF1<0的坐標(biāo)是(

)A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<013．（2023年四川省宜賓中考數(shù)學(xué)真題）如圖，在平面直角坐標(biāo)系SKIPIF1<0中，點(diǎn)A、B分別在y，x軸上，SKIPIF1<0軸．點(diǎn)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(diǎn)，P為x正半軸上一點(diǎn)，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14．（2022·甘肅武威·統(tǒng)考中考真題）若一次函數(shù)y=kx?2的函數(shù)值y隨著自變量x值的增大而增大，則k=（寫出一個(gè)滿足條件的值）．15．（2021·黑龍江哈爾濱·統(tǒng)考中考真題）已知反比例函數(shù)SKIPIF1<0的圖象經(jīng)過點(diǎn)SKIPIF1<0，則SKIPIF1<0的值為．16．（2023年湖南省長沙市中考數(shù)學(xué)真題）如圖，在平面直角坐標(biāo)系中，點(diǎn)SKIPIF1<0在反比例函數(shù)SKIPIF1<0SKIPIF1<0SKIPIF1<0為常數(shù)，SKIPIF1<0，SKIPIF1<0的圖象上，過點(diǎn)SKIPIF1<0作SKIPIF1<0軸的垂線，垂足為SKIPIF1<0，連接SKIPIF1<0．若SKIPIF1<0的面積為SKIPIF1<0，則SKIPIF1<0．

17．（2023年四川省成都市數(shù)學(xué)中考真題）若點(diǎn)SKIPIF1<0都在反比例函數(shù)SKIPIF1<0的圖象上，則SKIPIF1<0SKIPIF1<0（填“SKIPIF1<0”或“SKIPIF1<0”）．18．（2023年四川省達(dá)州市中考數(shù)學(xué)真題）如圖，一次函數(shù)SKIPIF1<0與反比例函數(shù)SKIPIF1<0的圖象相交于SKIPIF1<0兩點(diǎn)，以SKIPIF1<0為邊作等邊三角形SKIPIF1<0，若反比例函數(shù)SKIPIF1<0的圖象過點(diǎn)SKIPIF1<0，則SKIPIF1<0的值為．

19．（2023年四川省樂山市中考數(shù)學(xué)真題）定義：若x，y滿足SKIPIF1<0且SKIPIF1<0（t為常數(shù)），則稱點(diǎn)SKIPIF1<0為“和諧點(diǎn)”．（1）若SKIPIF1<0是“和諧點(diǎn)”，則SKIPIF1<0．（2）若雙曲線SKIPIF1<0存在“和諧點(diǎn)”，則k的取值范圍為．20．（2023年四川省內(nèi)江市中考數(shù)學(xué)真題）如圖，在平面直角坐標(biāo)系中，O為坐標(biāo)原點(diǎn)，SKIPIF1<0垂直于x軸，以SKIPIF1<0為對(duì)稱軸作SKIPIF1<0的軸對(duì)稱圖形，對(duì)稱軸SKIPIF1<0與線段SKIPIF1<0相交于點(diǎn)F，點(diǎn)D的對(duì)應(yīng)點(diǎn)B恰好落在反比例函數(shù)SKIPIF1<0的圖象上，點(diǎn)O、E的對(duì)應(yīng)點(diǎn)分別是點(diǎn)C、A．若點(diǎn)A為SKIPIF1<0的中點(diǎn)，且SKIPIF1<0，則k的值為．

21．（2019·四川眉山·統(tǒng)考中考真題）如圖，反比例函數(shù)SKIPIF1<0的圖象經(jīng)過矩形SKIPIF1<0對(duì)角線的交點(diǎn)SKIPIF1<0，分別交SKIPIF1<0，SKIPIF1<0于點(diǎn)SKIPIF1<0、SKIPIF1<0．若四邊形SKIPIF1<0的面積為12，則SKIPIF1<0的值為．22．（2023年四川省自貢市中考數(shù)學(xué)真題）如圖，直線SKIPIF1<0與x軸，y軸分別交于A，B兩點(diǎn)，點(diǎn)D是線段AB上一動(dòng)點(diǎn)，點(diǎn)H是直線SKIPIF1<0上的一動(dòng)點(diǎn)，動(dòng)點(diǎn)SKIPIF1<0，連接SKIPIF1<0．當(dāng)SKIPIF1<0取最小值時(shí)，SKIPIF1<0的最小值是．

三、解答題23．（2021·青海西寧·統(tǒng)考中考真題）如圖，正比例函數(shù)SKIPIF1<0與反比例函數(shù)SKIPIF1<0的圖象交于點(diǎn)A，SKIPIF1<0軸于點(diǎn)B，延長AB至點(diǎn)C，連接SKIPIF1<0．若SKIPIF1<0，SKIPIF1<0．（1）求SKIPIF1<0的長和反比例函數(shù)的解析式；（2）將SKIPIF1<0繞點(diǎn)SKIPIF1<0旋轉(zhuǎn)90°，請(qǐng)直接寫出旋轉(zhuǎn)后點(diǎn)A的對(duì)應(yīng)點(diǎn)A'的坐標(biāo)．24．（2022·重慶·統(tǒng)考中考真題）反比例函數(shù)SKIPIF1<0的圖象如圖所示，一次函數(shù)SKIPIF1<0（SKIPIF1<0）的圖象與SKIPIF1<0的圖象交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，

(1)求一次函數(shù)的表達(dá)式，并在所給的平面直角坐標(biāo)系中面出該函數(shù)的圖象；(2)觀察圖象，直接寫出不等式SKIPIF1<0的解集；(3)一次函數(shù)SKIPIF1<0的圖象與x軸交于點(diǎn)C，連接SKIPIF1<0，求SKIPIF1<0的面積．25．（2023年湖南省湘潭市中考數(shù)學(xué)真題）如圖，點(diǎn)A的坐標(biāo)是SKIPIF1<0，點(diǎn)B的坐標(biāo)是SKIPIF1<0，點(diǎn)C為SKIPIF1<0中點(diǎn)，將SKIPIF1<0繞著點(diǎn)B逆時(shí)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(diǎn)SKIPIF1<0，求該反比例函數(shù)的表達(dá)式；(2)一次函數(shù)圖像經(jīng)過A、SKIPIF1<0兩點(diǎn)，求該一次函數(shù)的表達(dá)式．26．（2023年四川省廣安市中考數(shù)學(xué)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(diǎn)SKIPIF1<0，與SKIPIF1<0軸交于點(diǎn)SKIPIF1<0．

(1)求一次函數(shù)和反比例函數(shù)的解析式．(2)點(diǎn)SKIPIF1<0在SKIPIF1<0軸上，SKIPIF1<0是以SKIPIF1<0為腰的等腰三角形，請(qǐng)直接寫出點(diǎn)SKIPIF1<0的坐標(biāo)．27．（2023年四川省宜賓中考數(shù)學(xué)真題）如圖，在平面直角坐標(biāo)系SKIPIF1<0中，等腰直角三角形SKIPIF1<0的直角頂點(diǎn)SKIPIF1<0，頂點(diǎn)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(dá)式和直線SKIPIF1<0所對(duì)應(yīng)的一次函數(shù)的表達(dá)式；(2)在x軸上是否存在一點(diǎn)P，使SKIPIF1<0周長的值最?。舸嬖?，求出最小值；若不存在，請(qǐng)說明理由．28．（2023年四川省眉山市中考數(shù)學(xué)真題）如圖，在平面直角坐標(biāo)系SKIPIF1<0中，直線SKIPIF1<0與x軸交于點(diǎn)SKIPIF1<0，與y軸交于點(diǎn)SKIPIF1<0，與反比例函數(shù)SKIPIF1<0在第四象限內(nèi)的圖象交于點(diǎn)SKIPIF1<0．

(1)求反比例函數(shù)的表達(dá)式：(2)當(dāng)SKIPIF1<0時(shí)，直接寫出x的取值范圍；(3)在雙曲線SKIPIF1<0上是否存在點(diǎn)P，使SKIPIF1<0是以點(diǎn)A為直角頂點(diǎn)的直角三角形？若存在，求出點(diǎn)P的坐標(biāo)；若不存在，請(qǐng)說明理由．29．（2023年四川省內(nèi)江市中考數(shù)學(xué)真題）如圖，在平面直角坐標(biāo)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(diǎn)，直線SKIPIF1<0與x軸相交于點(diǎn)C，連接SKIPIF1<0．

(1)求一次函數(shù)與反比例函數(shù)的表達(dá)式；(2)當(dāng)SKIPIF1<0時(shí)，請(qǐng)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(diǎn)B作SKIPIF1<0平行于x軸，交SKIPIF1<0于點(diǎn)D，求梯形SKIPIF1<0的面積．30．（2023年四川省廣元市中考真題數(shù)學(xué)試題）如圖，已知一次函數(shù)SKIPIF1<0的圖象與反比例函數(shù)SKIPIF1<0的圖象交于SKIPIF1<0，B兩點(diǎn)，與x軸交于點(diǎn)C，將直線SKIPIF1<0沿y軸向上平移3個(gè)單位長度后與反比例函數(shù)圖象交于點(diǎn)D，E．

(1)求k，m的值及C點(diǎn)坐標(biāo)；(2)連接SKIPIF1<0，SKIPIF1<0，求SKIPIF1<0的面積．31．（2023年四川省涼山州數(shù)學(xué)中考真題）閱讀理解題：閱讀材料：如圖1，四邊形SKIPIF1<0是矩形，SKIPIF1<0是等腰直角三角形，記SKIPIF1<0為SKIPIF1<0、SKIPIF1<0為SKIPIF1<0，若SKIPIF1<0，則SKIPIF1<0．

證明：設(shè)SKIPIF1<0，∵SKIPIF1<0，∴SKIPIF1<0，易證SKIPIF1<0∴SKIPIF1<0，∴SKIPIF1<0∴SKIPIF1<0，若SKIPIF1<0時(shí)，當(dāng)SKIPIF1<0，則SKIPIF1<0．同理：若SKIPIF1<0時(shí)，當(dāng)SKIPIF1<0，則SKIPIF1<0．根據(jù)上述材料，完成下列問題：如圖2，直線SKIPIF1<0與反比例函數(shù)SKIPIF1<0的圖象交于點(diǎn)SKIPIF1<0，與SKIPIF1<0軸交于點(diǎn)SKIPIF1<0．將直線SKIPIF1<0繞點(diǎn)SKIPIF1<0順時(shí)針旋轉(zhuǎn)SKIPIF1<0后的直線與SKIPIF1<0軸交于點(diǎn)SKIPIF1<0，過點(diǎn)SKIPIF1<0作SKIPIF1<0軸于點(diǎn)SKIPIF1<0，過點(diǎn)SKIPIF1<0作SKIPIF1<0軸于點(diǎn)SKIPIF1<0，已知SKIPIF1<0．

(1)求反比例函數(shù)的解析式；(2)直接寫出SKIPIF1<0的值；(3)求直線SKIPIF1<0的解析式．32．（2023·廣東梅州·統(tǒng)考一模）如圖，一次函數(shù)SKIPIF1<0與反比例函數(shù)SKIPIF1<0的圖象相交于A，B兩點(diǎn)，點(diǎn)A的橫坐標(biāo)為2，點(diǎn)B的橫坐標(biāo)為SKIPIF1<0，則不等式SKIPIF1<0的解集是（

）A．SKIPIF1<0或SKIPIF1<0 B．SKIPIF1<0或SKIPIF1<0 C．SKIPIF1<0或SKIPIF1<0 D．SKIPIF1<033．（2023·湖北鄂州·統(tǒng)考二模）數(shù)形結(jié)合是數(shù)學(xué)中的一種重要思想方法，在解題中運(yùn)用數(shù)形結(jié)合常常可以優(yōu)化解題思路，簡化解題過程．如圖，直線SKIPIF1<0與雙曲線SKIPIF1<0相交于點(diǎn)SKIPIF1<0．根據(jù)圖象可知關(guān)于SKIPIF1<0的方程SKIPIF1<0的解是（

）

A．SKIPIF1<0或1 B．SKIPIF1<0或2 C．1或2 D．SKIPIF1<0或SKIPIF1<034．（2023·陜西寶雞·統(tǒng)考三模）一次函數(shù)SKIPIF1<0的圖象不經(jīng)過第三象限，則（

）A．SKIPIF1<0，SKIPIF1<0 B．SKIPIF1<0，SKIPIF1<0 C．SKIPIF1<0，SKIPIF1<0 D．SKIPIF1<0，SKIPIF1<035．（2023·寧夏銀川·?？级＃└鶕?jù)如圖所示的二次函數(shù)SKIPIF1<0的圖象，判斷反比例函數(shù)SKIPIF1<0與一次函數(shù)SKIPIF1<0的圖象大致是（

）A． B． C． D．36．（2023·湖南永州·?？既＃┤鬝KIPIF1<0，則一次函數(shù)SKIPIF1<0與反比例函數(shù)SKIPIF1<0在同一直角坐標(biāo)系中的圖象大致可能是（）A． B．

C．

D．

37．（2023·北京順義·統(tǒng)考二模）某超市一種干果現(xiàn)在的售價(jià)是每袋SKIPIF1<0元，每星期可賣出SKIPIF1<0袋，經(jīng)市場調(diào)研發(fā)現(xiàn)，如果在一定范圍內(nèi)調(diào)整價(jià)格，每漲價(jià)SKIPIF1<0元，每星期就少賣出SKIPIF1<0袋．已知這種干果的進(jìn)價(jià)為每袋SKIPIF1<0元，設(shè)每袋漲價(jià)SKIPIF1<0（元），每星期的銷售量為SKIPIF1<0（袋），每星期銷售這種干果的利潤為SKIPIF1<0（元）．則SKIPIF1<0與SKIPIF1<0，SKIPIF1<0與SKIPIF1<0滿足的函數(shù)關(guān)系分別是（

）A．一次函數(shù)，二次函數(shù) B．一次函數(shù)，反比例函數(shù)C．反比例函數(shù)，二次函數(shù) D．反比例函數(shù)，一次函數(shù)38．（2023·江蘇南京·統(tǒng)考二模）若一個(gè)數(shù)SKIPIF1<0大于它的倒數(shù)，結(jié)合SKIPIF1<0和SKIPIF1<0的圖象（如圖），可知SKIPIF1<0的取值范圍是．

39．（2023·湖南長沙·校聯(lián)考二模）反比例函數(shù)SKIPIF1<0的圖象如圖所示，點(diǎn)SKIPIF1<0是該函數(shù)圖象上一點(diǎn)，SKIPIF1<0垂直于SKIPIF1<0軸，垂足是點(diǎn)SKIPIF1<0，如果SKIPIF1<0，則SKIPIF1<0的值為．40．（2023·湖北鄂州·統(tǒng)考二模）如圖，點(diǎn)SKIPIF1<0在雙曲線SKIPIF1<0上，點(diǎn)SKIPIF1<0在雙曲線SKIPIF1<0上，SKIPIF1<0軸，已知點(diǎn)SKIPIF1<0的橫坐標(biāo)分別為SKIPIF1<0與SKIPIF1<0的面積之和為SKIPIF1<0，則SKIPIF1<0的值為．

41．（2023·湖北十堰·統(tǒng)考一模）如圖，在平面直角坐標(biāo)系SKIPIF1<0中，已知正比例函數(shù)SKIPIF1<0的圖象與反比例函數(shù)SKIPIF1<0的圖象交于SKIPIF1<0兩點(diǎn)．

(1)求反比例函數(shù)的解析式和點(diǎn)SKIPIF1<0的坐標(biāo)；(2)結(jié)合圖象，請(qǐng)直接寫出不等式SKIPIF1<0的解集．42．（2023·江蘇泰州·統(tǒng)考二模）在平面直角坐標(biāo)系SKIPIF1<0中，函數(shù)SKIPIF1<0和直線SKIPIF1<0（k為常數(shù)，且SKIPIF1<0）的圖像如圖所示，若函數(shù)SKIPIF1<0與SKIPIF1<0的圖像有一個(gè)交點(diǎn)SKIPIF1<0．

(1)求m，k的值；(2)過動(dòng)點(diǎn)SKIPIF1<0作平行于x軸的直線，分別交函數(shù)SKIPIF1<0和SKIPIF1<0的圖像于點(diǎn)B、C，在點(diǎn)P的運(yùn)動(dòng)過程中，點(diǎn)P、B、C三點(diǎn)中一點(diǎn)是另外兩點(diǎn)的所連線段的中點(diǎn)，求此時(shí)n的值．43．（2023·寧夏銀川·校考二模）如圖，正比例函數(shù)SKIPIF1<0與反比例函數(shù)SKIPIF1<0的圖象交于點(diǎn)A，過點(diǎn)A作SKIPIF1<0軸于點(diǎn)B，SKIPIF1<0，點(diǎn)C在線段SKIPIF1<0上，且SKIPIF1<0．（1）求k的值及線段SKIPIF1<0的長；（2）點(diǎn)P為B點(diǎn)上方y(tǒng)軸上一點(diǎn)，當(dāng)SKIPIF1<0與SKIPIF1<0的面積相等時(shí)，請(qǐng)求出點(diǎn)P的坐標(biāo)．44．（2023·安徽蚌埠·統(tǒng)考三模）如圖，直線SKIPIF1<0與反比例函數(shù)SKIPIF1<0在第一條限內(nèi)交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)，SKIPIF1<0軸上的點(diǎn)SKIPIF1<0滿足SKIPIF1<0．

(1)若點(diǎn)SKIPIF1<0坐標(biāo)為SKIPIF1<0，求點(diǎn)SKIPIF1<0的坐標(biāo)；(2)若SKIPIF1<0的面積為SKIPIF1<0，求實(shí)數(shù)SKIPIF1<0的值；(3)設(shè)點(diǎn)SKIPIF1<0，SKIPIF1<0的坐標(biāo)分別為SKIPIF1<0，SKIPIF1<0，求SKIPIF1<0的值．45．（2023·廣東梅州·統(tǒng)考一模）如圖，一次函數(shù)SKIPIF1<0的圖象與反比例函數(shù)SKIPIF1<0的圖像相交于SKIPIF1<0、SKIPIF1<0兩點(diǎn)．（1）求一次函數(shù)和反比例函數(shù)的解析式；（2）根據(jù)圖象，直接寫出滿足SKIPIF1<0的SKIPIF1<0的取值范圍；（3）若點(diǎn)SKIPIF1<0在線段SKIPIF1<0上，且SKIPIF1<0，求點(diǎn)SKIPIF1<0的坐標(biāo)．46．（2023·廣東廣州·廣州市真光中學(xué)?？级＃┤鐖D，雙曲線SKIPIF1<0與直線SKIPIF1<0交于點(diǎn)SKIPIF1<0、SKIPIF1<0，與兩坐標(biāo)軸分別交于點(diǎn)SKIPIF1<0，已知點(diǎn)SKIPIF1<0，連接SKIPIF1<0．

(1)求SKIPIF1<0的面積；(2)作直線SKIPIF1<0，將直線SKIPIF1<0向上平移SKIPIF1<0個(gè)單位后，與雙曲線SKIPIF1<0有唯一交點(diǎn)，求SKIPIF1<0的值．47．（2023·山東菏澤·統(tǒng)考二模）如圖，反比例函數(shù)SKIPIF1<0與一次函數(shù)SKIPIF1<0的圖象交于點(diǎn)SKIPIF1<0，點(diǎn)SKIPIF1<0，一次函數(shù)SKIPIF1<0與y軸交于點(diǎn)C．(1)求反比例函數(shù)和一次函數(shù)解析式；(2)連接SKIPIF1<0，求SKIPIF1<0的面積；(3)如圖2，點(diǎn)E是反比例函數(shù)圖象上A點(diǎn)右側(cè)一點(diǎn)，連接SKIPIF1<0，把線段SKIPIF1<0繞點(diǎn)A順時(shí)針旋轉(zhuǎn)SKIPIF1<0，點(diǎn)E的對(duì)應(yīng)點(diǎn)F恰好也落在這個(gè)反比例函數(shù)的圖象上，求點(diǎn)E的坐標(biāo)．48．（2023·山東濟(jì)南·統(tǒng)考三模）如圖，一次函數(shù)SKIPIF1<0的圖像與x軸交于點(diǎn)SKIPIF1<0，與反比例函數(shù)SKIPIF1<0的圖像交于點(diǎn)SKIPIF1<0，過直線SKIPIF1<0上的點(diǎn)B作SKIPIF1<0軸于點(diǎn)C，與反比例函數(shù)交于點(diǎn)SKIPIF1<0，連接SKIPIF1<0，SKIPIF1<0．

(1)求k的值與B點(diǎn)坐標(biāo)；(2)求SKIPIF1<0；(3)若點(diǎn)P是直線SKIPIF1<0上的動(dòng)點(diǎn)，是否存在點(diǎn)P，使得SKIPIF1<0與SKIPIF1<0相似？若存在，求出此時(shí)P點(diǎn)的坐標(biāo)；若不存在，請(qǐng)說明理由．49．（2023·貴州貴陽·統(tǒng)考二模）已知一次函數(shù)SKIPIF1<0的圖象與反比例函數(shù)SKIPIF1<0的圖象相交于點(diǎn)SKIPIF1<0，SKIPIF1<0．

(1)求一次函數(shù)的表達(dá)式；(2)直接寫出不等式SKIPIF1<0的解集．50．（2023·四川攀枝花·統(tǒng)考二模）如圖，在平面直角坐標(biāo)系中，一次函數(shù)SKIPIF1<0的圖象與SKIPIF1<0軸負(fù)半軸交于點(diǎn)SKIPIF1<0，與SKIPIF1<0軸交于SKIPIF1<0點(diǎn)，與反比例函數(shù)SKIPIF1<0交于SKIPIF1<0，SKIPIF1<0兩點(diǎn)．(1)求一次函數(shù)的解析式，并畫出一次函數(shù)的圖象；(2)請(qǐng)直接寫出不等式SKIPIF1<0的解集；(3)求SKIPIF1<0的面積．51．（2023·山東菏澤·統(tǒng)考三模）如圖，反比例函數(shù)SKIPIF1<0與一次函數(shù)SKIPIF1<0的圖象交于點(diǎn)SKIPIF1<0，點(diǎn)SKIPIF1<0，一次函數(shù)SKIPIF1<0與SKIPIF1<0軸相交于點(diǎn)SKIPIF1<0．

(1)求反比例函數(shù)和一次函數(shù)的表達(dá)式，(2)連接SKIPIF1<0，SKIPIF1<0，求SKIPIF1<0的面積．52．（2023·江蘇蘇州·?？级＃┤鐖D，直線SKIPIF1<0與反比例函數(shù)SKIPIF1<0的圖像相交于點(diǎn)A和點(diǎn)SKIPIF1<0，與x軸的正半軸相交于點(diǎn)B．(1)求k的值；(2)連接SKIPIF1<0，若點(diǎn)C為線段SKIPIF1<0的中點(diǎn)，求SKIPIF1<0的面積．53．（2023·河南新鄉(xiāng)·校聯(lián)考二模）如圖，平行于SKIPIF1<0軸的直尺SKIPIF1<0一部分SKIPIF1<0與雙曲線SKIPIF1<0交于點(diǎn)SKIPIF1<0和SKIPIF1<0，與SKIPIF1<0軸交于點(diǎn)SKIPIF1<0和SKIPIF1<0，點(diǎn)SKIPIF1<0和SKIPIF1<0的刻度分別為SKIPIF1<0和SKIPIF1<0，直尺的寬度為SKIPIF1<0，SKIPIF1<0(注：平面直角坐標(biāo)系內(nèi)一個(gè)單位長度為SKIPIF1<0)．

(1)求反比例函數(shù)解析式；(2)若經(jīng)過SKIPIF1<0，SKIPIF1<0兩點(diǎn)的直線關(guān)系式為SKIPIF1<0，請(qǐng)直接寫出不等式SKIPIF1<0的解集；(3)求梯形SKIPIF1<0的面積．54．（2023·江蘇無錫·?？级＃┒x：經(jīng)過函數(shù)圖像上的一點(diǎn)作x軸的平行線，將平行線上方的圖像沿平行線向下翻折形成新的函數(shù)圖像，我們把滿足這種情況的函數(shù)圖像稱為經(jīng)過這一點(diǎn)的“折疊函數(shù)”．【基本應(yīng)用】(1)如圖，點(diǎn)SKIPIF1<0、SKIPIF1<0、SKIPIF1<0均在直線l上．

①請(qǐng)使用無刻度的直尺和圓規(guī)作出經(jīng)過點(diǎn)C的“折疊函數(shù)”與x軸的交點(diǎn)D（異于點(diǎn)A）；②求出經(jīng)過點(diǎn)A、C、D的二次函數(shù)表達(dá)式；(2)在（1）的條件下，點(diǎn)SKIPIF1<0為二次函數(shù)圖像上一動(dòng)點(diǎn)，若經(jīng)過點(diǎn)P的“折疊函數(shù)”與x軸至少有3個(gè)交點(diǎn)，求a的取值范圍．【創(chuàng)新應(yīng)用】(3)如果反比例函數(shù)SKIPIF1<0的圖像上有一點(diǎn)SKIPIF1<0，則經(jīng)過點(diǎn)M的“折疊函數(shù)”與x軸的交點(diǎn)坐標(biāo)為________．55.（2023·廣東廣州·廣州市真光中學(xué)?？级＃┤鐖D，雙曲線SKIPIF1<0與直線SKIPIF1<0交于點(diǎn)SKIPIF1<0、SKIPIF1<0，與兩坐標(biāo)軸分別交于點(diǎn)SKIPIF1<0，已知點(diǎn)SKIPIF1<0，連接SKIPIF1<0