配套习题- 反比例函数图像中的规律探究问题 -【青果学院】

挑战习题

1/5单选题

难度：

1.如图，在反比例函数y=

（x＞0）的图象上，有点P₁、P₂、P₃、P₄，它们的横坐标依次为1，2，3，4. 分别过这些点作x轴与y轴的垂线，图中所构成的阴影部分的面积从左到右依次为S₁、S₂、S₃，则S₁+S₂+S₃=（　　）

A	1
B	1.5
C	2
D	无法确定

提示1：: IOagueaNruWPjeavlOS+i+WHveaVsOeahOWHoOS9leaEj+S5ieWPr+efpeWbvuS4reaJgOaehOaIkOeahOmYtOW9semDqOWIhueahOmdouenr+WSjOato+WlveaYr+S7jueCuVA8c3ViPjE8L3N1Yj7lkJF46L2077yMeei9tOW8leWegue6v+aehOaIkOeahOmVv+aWueW9oumdouenr+WHj+WOu+acgOS4i+aWueeahOmVv+aWueW9oueahOmdouenry4=

正确答案：Qg==

6Kej77ya55Sx6aKY5oSP5Y+v55+l54K5UDxzdWI+MTwvc3ViPuOAgVA8c3ViPjI8L3N1Yj7jgIFQPHN1Yj4zPC9zdWI+44CBUDxzdWI+NDwvc3ViPuWdkOagh+WIhuWIq+S4uu+8mu+8iDHvvIwy77yJ77yM77yIMu+8jDHvvInvvIzvvIgz77yMPGltZyB3aWR0aD03IGhlaWdodD00MiBzcmM9Imh0dHBzOi8vcDIucWluZ2d1by5jb20vRzEvTTAwLzkzLzE4L3JCQUNFMVBiWWpqUUtNVVhBQUFCT3lpVnYwMDE3Ni5wbmciPu+8ie+8jO+8iDTvvIw8aW1nIHdpZHRoPTcgaGVpZ2h0PTQyIHNyYz0iaHR0cHM6Ly9wMi5xaW5nZ3VvLmNvbS9HMS9NMDAvOTMvMTgvckJBQ0UxUGJZakh3MjI3a0FBQUJKRHRSSFFrNDQ4LnBuZyI+77yJLiA8YnI+4oi055Sx5Y+N5q+U5L6L5Ye95pWw55qE5Yeg5L2V5oSP5LmJ5Y+v55+l77yaUzxzdWI+MTwvc3ViPitTPHN1Yj4yPC9zdWI+K1M8c3ViPjM8L3N1Yj49Mi0xw5c8aW1nIHdpZHRoPTcgaGVpZ2h0PTQyIHNyYz0iaHR0cHM6Ly9wMi5xaW5nZ3VvLmNvbS9HMS9NMDAvOTMvMTgvckJBQ0UxUGJZakh3MjI3a0FBQUJKRHRSSFFrNDQ4LnBuZyI+PTxpbWcgd2lkdGg9NyBoZWlnaHQ9NDIgc3JjPSJodHRwczovL3AyLnFpbmdndW8uY29tL0cxL00wMC81NS85OC9yQkFDRkZQYllqandWRkt6QUFBQk4xdE1xYUU5MDEucG5nIj49MS41LiA8YnI+5pWF6YCJQi4g

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2/5单选题

难度：

2.如图，P₁、P₂、P₃是双曲线上的三点. 过这三点分别作y轴的垂线，得到三个三角形P₁A₁0，P₂A₂0，P₃A₃0，设它们的面积分别是S₁、S₂、S₃，则（　　）

A	S₁＜S₂＜S₃
B	S₂＜S₁＜S₃
C	S₁＜S₃＜S₂
D	S₁=S₂=S₃

提示1：: IOagueaNruWPjOabsue6v+eahOWbvuixoeS4iueahOeCueS4juWOn+eCueaJgOi/nueahOe6v+auteOAgeWdkOagh+i9tOOAgeWQkeWdkOagh+i9tOS9nOWegue6v+aJgOWbtOaIkOeahOebtOinkuS4ieinkuW9oumdouenr1PnmoTlhbPns7tTPTxpbWcgd2lkdGg9NyBoZWlnaHQ9NDIgc3JjPSJodHRwczovL3AyLnFpbmdndW8uY29tL0cxL00wMC85My8xOC9yQkFDRTFQYllqSHcyMjdrQUFBQkpEdFJIUWs0NDgucG5nIj58a3zljbPlj6/liKTmlq0=

正确答案：RA==

6Kej77ya5Zug5Li66L+H5Y+M5puy57q/5LiK5Lu75oSP5LiA54K55LiO5Y6f54K55omA6L+e55qE57q/5q6144CB5Z2Q5qCH6L2044CB5ZCR5Z2Q5qCH6L205L2c5Z6C57q/5omA5Zu05oiQ55qE55u06KeS5LiJ6KeS5b2i6Z2i56evU+aYr+S4quWumuWAvO+8jOWNs1M9PGltZyB3aWR0aD03IGhlaWdodD00MiBzcmM9Imh0dHBzOi8vcDIucWluZ2d1by5jb20vRzEvTTAwLzkzLzE4L3JCQUNFMVBiWWpIdzIyN2tBQUFCSkR0UkhRazQ0OC5wbmciPnxrfO+8jOaJgOS7pVM8c3ViPjE8L3N1Yj49UzxzdWI+Mjwvc3ViPj1TPHN1Yj4zPC9zdWI+LiA8YnI+5pWF6YCJRC4g

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3/5单选题

难度：

3.在反比例函数y＝

（x＞0）的图象上，有一系列点P₁、P₂、P₃、…、Pn，若P₁的横坐标为2，且以后每点的横坐标与它前一个点的横坐标的差都为2. 现分别过点P₁、P₂、P₃、…、P_n作x轴与y轴的垂线段，构成若干个长方形如图所示，将图中阴影部分的面积从左到右依次记为S₁、S₂、S₃、…、S_n，则

( )

A	1
B
C
D

提示1：: IOaxguW+l1A8c3ViPjE8L3N1Yj7nmoTlnZDmoIflvpfliLDnn6nlvaJQPHN1Yj4xPC9zdWI+QU9C55qE6Z2i56ev

提示2：: IOiAjOaKiuaJgOacieeahOmYtOW9semDqOWIhuW5s+enu+WIsOW3pui+ue+8jOmYtOW9semDqOWIhueahOmdouenr+S5i+WSjOWwseetieS6juefqeW9olA8c3ViPjE8L3N1Yj5BT0LnmoTpnaLnp6/vvIzljbPlj6/lvpfliLDnrZTmoYgu

正确答案：RA==

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4/5单选题

难度：

4.如图，在x轴的正半轴上依次截取OA₁=A₁A₂=A₂A₃=A₃A₄=A₄A₅，过点A₁、A₂、A₃、A₄、A₅分别作x轴的垂线与反比例函数y＝

（x≠0）的图象相交于点P₁、P₂、P₃、P₄、P₅，得直角三角形OP₁A₁、A₁P₂A₂、A₂P₃A₃、A₃P₃A₄、A₄P₅A₅，并设其面积分别为S₁、S₂、S₃、S₄、S₅，则S₁+S₂+S₃+S₄+S₅的值为（　　）

A	2
B	3
C
D

提示1：: IOeUseS6jui/h+WPjOabsue6v+S4iueahOS7u+aEj+S4gOeCueWIhuWIq+WQkeS4pOadoeWdkOagh+i9tOS9nOWegue6v++8jOS4juWdkOagh+i9tOWbtOaIkOeahOefqeW9oumdouenr+WwseetieS6jnxrfO+8jOWPr+WFiOeUsXxrfOS+neasoeihqOekuuWHuuWbvuS4reWQhOmYtOW9seS4ieinkuW9oueahOmdouenr++8jOWGjeebuOWKoOWNs+WPr+W+l+WIsOmdouenr+eahOWSjC4=

正确答案：Qw==

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5/5单选题

难度：

5.两个反比例函数y＝

，y＝−

的图象在第一象限，第二象限如图，点P₁、P₂、P₃…P₂₀₁₀在y＝

的图象上，它们的横坐标分别是有这样规律的一行数列1，3，5，7，9，11，…，过点P₁、P₂、P₃、…、P₂₀₁₀分别作x轴的平行线，与y＝−

的图象交点依次是Q₁、Q₂、Q₃、…、Q₂₀₁₀，则点Q₂₀₁₀的横坐标是（）

A	-8038
B	8038
C	-8036
D	8036

提示1：: IOagueaNrlA8c3ViPjIwMTA8L3N1Yj7lkoxRPHN1Yj4yMDEwPC9zdWI+55qE57q15Z2Q5qCH55u45ZCM5om+5Ye65o6S5YiX6KeE5b6L77yM5Luj5YWl5Y+N5q+U5L6L5Ye95pWw55qE6Kej5p6Q5byP5Y2z5Y+vLg==

正确答案：QQ==

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