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> 如图,已知反比例函数y=的图象经过点A(1,-3),一次函数y=kx+b的图象经过点A与点C(0,-4),且与反比例函数的图象相交于另一点B(3,n)。(1)试确定这两个函数的解析式;(2)求△-九年
如图,已知反比例函数y=的图象经过点A(1,-3),一次函数y=kx+b的图象经过点A与点C(0,-4),且与反比例函数的图象相交于另一点B(3,n)。(1)试确定这两个函数的解析式;(2)求△-九年
题目简介
如图,已知反比例函数y=的图象经过点A(1,-3),一次函数y=kx+b的图象经过点A与点C(0,-4),且与反比例函数的图象相交于另一点B(3,n)。(1)试确定这两个函数的解析式;(2)求△-九年
题目详情
如图,已知反比例函数y=
的图象经过点A(1,-3),一次函数y = kx + b的图象经过点A与点C(0,-4),且与反比例函数的图象相交于另一点B(3,n)。
(1)试确定这两个函数的解析式;
(2)求△AOB的面积;
(3)根据图形直接写出反比例函数值大于一次函数值时自变量的取值范围。
题型:解答题
难度:中档
来源:重庆市月考题
答案
解:(1)∵
的图象经过点
∴
,即
∴反比例函数解析式为:
又∵
∴
, 即:B点坐标为(3, -1)
将
,
代入y = kx + b得:
∴一次函数解析式为:y = x - 4
(2)
=
=
= 4
(3)由图象可知:当x<0或1<x<3时,反比例函数值大于一次函数值。
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题目简介
如图,已知反比例函数y=的图象经过点A(1,-3),一次函数y=kx+b的图象经过点A与点C(0,-4),且与反比例函数的图象相交于另一点B(3,n)。(1)试确定这两个函数的解析式;(2)求△-九年
题目详情
(1)试确定这两个函数的解析式;
(2)求△AOB的面积;
(3)根据图形直接写出反比例函数值大于一次函数值时自变量的取值范围。
答案
∴
∴反比例函数解析式为:
又∵
∴
将
∴一次函数解析式为:y = x - 4
(2)
(3)由图象可知:当x<0或1<x<3时,反比例函数值大于一次函数值。