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第二十七章　反比例函數
27. 2 反比例函數的圖像和性質
第1課時　反比例函數的圖像
INCLUDEPICTURE"復習回顧.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\復習回顧.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\復習回顧.tif" \* MERGEFORMATINET
1．正比例函數y＝kx(k≠0)的圖像如圖所示，則一次函數y＝kx－k的圖像大致是(　　)
2．已知反比例函數y＝，那么下列各點中在此函數圖像上的是(　　)
A．(－2，3) B．(－3，2) C．(－3，－2) D．(4，1)
3．畫函數圖像的步驟：________、________、________．
INCLUDEPICTURE"預習效果檢測.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\預習效果檢測.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\預習效果檢測.tif" \* MERGEFORMATINET
1．反比例函數y＝(k為常數，且k≠0)的圖像由分別位于________象限內的兩條________組成，這樣的曲線叫做雙曲線．
2．反比例函數y＝－的圖像大致是(　　)
3．在如圖所示的坐標系中，畫出反比例函數y＝－的圖像．
INCLUDEPICTURE"冊59.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊59.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊59.tif" \* MERGEFORMATINET
INCLUDEPICTURE"課堂導學.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\課堂導學.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\課堂導學.tif" \* MERGEFORMATINET
INCLUDEPICTURE"W21.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\W21.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\W21.tif" \* MERGEFORMATINET
知識點1 反比例函數的圖像及畫法INCLUDEPICTURE"L1.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\L1.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\L1.tif" \* MERGEFORMATINET 畫出反比例函數y＝－的大致圖像，結合圖像回答：
(1)當x＝2時，y的值；
(2)當1(3)當－1≤y<4且y≠0時，x的取值范圍．
　　　　　　　　　　　　　　　
變式1已知反比例函數y＝－.
(1)畫出這個反比例函數的圖像；
(2)利用所畫圖像求當y<2時，x的取值范圍；
(3)已知(－3，y1)，(－15，y2)，(1，y3)是所畫圖像上的三個點，比較y1，y2，y3的大小．
　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　
知識點2 反比例函數圖像上點的坐標特點INCLUDEPICTURE"L2.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\L2.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\L2.tif" \* MERGEFORMATINET [2023渭南一模已知正比例函數y＝ax(a為常數，a≠0)與反比例函數y＝的圖像的一個交點坐標為(1，m)，則另一個交點的坐標為______________．
　　　　　　　　　　　　　　　
變式2如圖，在平面直角坐標系xOy中，直線y＝3x與雙曲線y＝(m≠0)交于A，B兩點，若點A，B的橫坐標分別為x1，x2，則x1＋x2＝________．
INCLUDEPICTURE"冊60.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊60.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊60.tif" \* MERGEFORMATINET
第2課時　反比例函數的性質
INCLUDEPICTURE"復習回顧.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\復習回顧.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\復習回顧.tif" \* MERGEFORMATINET
1．關于一次函數y＝－2x－3，下列說法正確的是(　　)
A．圖像經過第一、二、四象限
B．當x>0時，y<－3
C．函數值y隨自變量x的增大而增大
D．圖像與y軸交于點
2．已知一次函數y＝kx＋b，函數值y隨自變量x的增大而減小，且kb<0，則函數y＝kx＋b的圖像大致是(　　)
INCLUDEPICTURE"預習效果檢測.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\預習效果檢測.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\預習效果檢測.tif" \* MERGEFORMATINET
1．對于反比例函數y＝，請完成以下表格．
表達式 圖像的位置 y隨x的變化情況
y＝ (k＞0) 圖像在第______、______象限內 在每個象限內，y的值隨x值的增大而______
y＝ (k＜0) 圖像在第______、______象限內 在每個象限內，y的值隨x值的增大而______
2.[2023哈爾濱期末]對于反比例函數y＝，下列說法不正確的是(　　)
A．點(2，1)在它的圖像上
B．它的圖像在第一、三象限
C．當x>0時，y隨x的增大而增大
D．當x<0時，y隨x的增大而減小
3．已知反比例函數y＝(k為常數)的圖像在第二、四象限，寫出一個符合條件的k的值：________．
4．若點A(x1，－6)，B(x2，－2)，C(x3，2)在反比例函數y＝的圖像上，則x1，x2，x3的大小關系是________________．
INCLUDEPICTURE"課堂導學.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\課堂導學.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\課堂導學.tif" \* MERGEFORMATINET
INCLUDEPICTURE"W21.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\W21.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\W21.tif" \* MERGEFORMATINET
知識點1 反比例函數的性質INCLUDEPICTURE"L1.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\L1.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\L1.tif" \* MERGEFORMATINET [2023沈陽期末]關于反比例函數y＝－，下列說法不正確的是(　　)
A．點(2 024，－1)在它的圖像上
B．它的圖像在第二、四象限
C．當x<0時，y隨x的增大而增大
D．當x>2時，y<－1 012
變式1－1反比例函數y＝的圖像在每個象限內，y隨x的增大而增大，則m的取值范圍是(　　)
A．m>－2 B．m≥－2 C．m<－2 D．m≤－2
變式1－2[2023宜昌中考]某反比例函數圖像上四個點的坐標分別為(－3，y1)，(－2，3)，(1，y2)，(2，y3)，則y1，y2，y3的大小關系為(　　)
A．y2＜y1＜y3 B．y3＜y2＜y1 C．y2＜y3＜y1 D．y1＜y3＜y2
　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　知識點2 反比例函數y＝(k≠0)的比例系數k的幾何意義INCLUDEPICTURE"L2.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\L2.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\L2.tif" \* MERGEFORMATINET [2023邵陽中考]如圖，矩形OABC的頂點B和正方形ADEF的頂點E都在反比例函數y＝(k≠0)的圖像上，點B的坐標為(2，4)，則點E的坐標為(　　)
INCLUDEPICTURE"冊70.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊70.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊70.tif" \* MERGEFORMATINET
A．(4，4)　 B．(2，2) C．(2，4) D．(4，2)
變式2如圖，矩形ABCD的邊CD在x軸上，頂點A在雙曲線y＝上，頂點B在雙曲線y＝上，求矩形ABCD的面積．
INCLUDEPICTURE"冊71.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊71.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\冊71.tif" \* MERGEFORMATINET
27. 2 反比例函數的圖像和性質
第1課時　反比例函數的圖像
INCLUDEPICTURE"復習回顧.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\復習回顧.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\復習回顧.tif" \* MERGEFORMATINET
1．A　2.C　3.列表；描點；連線
INCLUDEPICTURE"預習效果.tif" INCLUDEPICTURE "預習效果.tif" \* MERGEFORMAT INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\預習效果.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\預習效果.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\預習效果.tif" \* MERGEFORMATINET
1．兩個；曲線　2.C
3．解：列表如下：
x … －4 －2 －1 1 2 4 …
y … 1 2 4 －4 －2 －1 …
反比例函數y＝－的圖像如圖．
INCLUDEPICTURE"答100.tif" INCLUDEPICTURE "答100.tif" \* MERGEFORMAT INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\答100.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\答100.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\答100.tif" \* MERGEFORMATINET
INCLUDEPICTURE"課堂導學.tif" INCLUDEPICTURE "課堂導學.tif" \* MERGEFORMAT INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\課堂導學.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\課堂導學.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\課堂導學.tif" \* MERGEFORMATINET
例1　解：作出反比例函數y＝－的大致圖像如圖所示．
INCLUDEPICTURE"答101.tif" INCLUDEPICTURE "答101.tif" \* MERGEFORMAT INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\答101.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\答101.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\答101.tif" \* MERGEFORMATINET
(1)把x＝2代入y＝－，
得y＝－＝－2.
(2)當x＝1時，y＝－4；
當x＝4時，y＝－1.
根據圖像得，當1y的取值范圍為－4(3)當y＝－1時，x＝4；當y＝4時，x＝－1.
根據圖像得，當－1≤y<4且y≠0時，
x的取值范圍為x<－1或x≥4.
INCLUDEPICTURE"答102.tif" INCLUDEPICTURE "答102.tif" \* MERGEFORMAT INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\答102.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\答102.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\答102.tif" \* MERGEFORMATINET
變式1.解：(1)畫出圖像如圖所示．
(2)由圖像可知當y<2時，x＞0或x<－2.
(3)y1>y2>y3.
例2　(－1，2)　變式2.0
第2課時　反比例函數的性質
INCLUDEPICTURE"復習回顧.tif" INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\復習回顧.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\復習回顧.tif" \* MERGEFORMATINET
1．B　2.C
INCLUDEPICTURE"預習效果.tif" INCLUDEPICTURE "預習效果.tif" \* MERGEFORMAT INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\預習效果.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\預習效果.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\預習效果.tif" \* MERGEFORMATINET
1．一；三；減小；二；四；增大
2．C　3.－2(答案不唯一)　4.x2INCLUDEPICTURE"課堂導學.tif" INCLUDEPICTURE "課堂導學.tif" \* MERGEFORMAT INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\課堂導學.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\課堂導學.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\課件\\九數JJ河北（北京）\\課堂導學.tif" \* MERGEFORMATINET
例1　D　變式1－1.C　變式1－2.C　例2　D
變式2.解：設A，則B，
∴S矩形ADOE＝x·＝1，S矩形BCOE＝3x·＝3，
∴S矩形ABCD＝S矩形BCOE－S矩形ADOE＝3－1＝2.

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