【答案】
分析:(1)解兩條直線的解析式組成的方程組的解,即可求得交點(diǎn)M的坐標(biāo),在y=-x+6中,令y=0即可求得點(diǎn)N的橫坐標(biāo),則N的坐標(biāo)即可求解;
(2)分成0≤t≤1,1<t≤4,4<t≤5,5<t≤6,6<t≤7五種情況,利用三角形的面積公式和梯形的面積公式,即可求得函數(shù)的解析式;
(3)分別求得每種情況下函數(shù)的最值或函數(shù)值的范圍,即可確定.
解答:解:(1)解方程組
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131101185455889891572/SYS201311011854558898915027_DA/0.png)
,
解得:
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131101185455889891572/SYS201311011854558898915027_DA/1.png)
,
則M的坐標(biāo)是:(4,2).
在解析式y(tǒng)=-x+6中,令y=0,解得:x=6,則N的坐標(biāo)是:(6,0).
(2)當(dāng)0≤t≤1時,重合部分是一個三角形,OB=t,則高是
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131101185455889891572/SYS201311011854558898915027_DA/2.png)
t,則面積是
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131101185455889891572/SYS201311011854558898915027_DA/3.png)
×t•
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131101185455889891572/SYS201311011854558898915027_DA/4.png)
t=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131101185455889891572/SYS201311011854558898915027_DA/5.png)
t
2;
當(dāng)1<t≤4時,重合部分是直角梯形,梯形的高是1,下底是:
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131101185455889891572/SYS201311011854558898915027_DA/6.png)
t,上底是:
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131101185455889891572/SYS201311011854558898915027_DA/7.png)
(t-1),根據(jù)梯形的面積公式可以得到:S=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131101185455889891572/SYS201311011854558898915027_DA/8.png)
[
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131101185455889891572/SYS201311011854558898915027_DA/9.png)
t+
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131101185455889891572/SYS201311011854558898915027_DA/10.png)
(t-1)]=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131101185455889891572/SYS201311011854558898915027_DA/11.png)
(t-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131101185455889891572/SYS201311011854558898915027_DA/12.png)
);
當(dāng)4<t≤5時,過M作x軸的垂線,則重合部分被垂線分成兩個直角梯形,兩個梯形的下底都是2,上底分別是:-t+6和
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131101185455889891572/SYS201311011854558898915027_DA/13.png)
(t-1),根據(jù)梯形的面積公式即可求得
S=-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131101185455889891572/SYS201311011854558898915027_DA/14.png)
t
2+
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131101185455889891572/SYS201311011854558898915027_DA/15.png)
t-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131101185455889891572/SYS201311011854558898915027_DA/16.png)
;
當(dāng)5<t≤6時,重合部分是直角梯形,與當(dāng)1<t≤4時,重合部分是直角梯形的計(jì)算方法相同,則S=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131101185455889891572/SYS201311011854558898915027_DA/17.png)
(13-2t);
當(dāng)6<t≤7時,重合部分是直角三角形,則與當(dāng)0≤t≤1時,解法相同,可以求得S=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131101185455889891572/SYS201311011854558898915027_DA/18.png)
(7-t)
2.
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131101185455889891572/SYS201311011854558898915027_DA/images19.png)
則:S=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131101185455889891572/SYS201311011854558898915027_DA/19.png)
;
(3)在0≤t≤1時,函數(shù)值y隨t的增大而增大,則當(dāng)t=1時,取得最大值是:
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131101185455889891572/SYS201311011854558898915027_DA/20.png)
;
當(dāng)1<t≤4,函數(shù)值y隨t的增大而增大,則當(dāng)t=4時,取得最大值是:
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131101185455889891572/SYS201311011854558898915027_DA/21.png)
(4-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131101185455889891572/SYS201311011854558898915027_DA/22.png)
)=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131101185455889891572/SYS201311011854558898915027_DA/23.png)
;
當(dāng)4<t≤5時,是二次函數(shù),對稱軸t=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131101185455889891572/SYS201311011854558898915027_DA/24.png)
,則最大值是:-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131101185455889891572/SYS201311011854558898915027_DA/25.png)
×(
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131101185455889891572/SYS201311011854558898915027_DA/26.png)
)
2+
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131101185455889891572/SYS201311011854558898915027_DA/27.png)
×
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131101185455889891572/SYS201311011854558898915027_DA/28.png)
-
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131101185455889891572/SYS201311011854558898915027_DA/29.png)
=
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131101185455889891572/SYS201311011854558898915027_DA/30.png)
;
當(dāng)5<t≤6時,函數(shù)值y隨t的增大而減小,無最大值;
同理,當(dāng)6<t≤7時,y隨t的增大而減小,無最大值.
總之,函數(shù)的最大值是:
![](http://thumb.zyjl.cn/pic6/res/czsx/web/STSource/20131101185455889891572/SYS201311011854558898915027_DA/31.png)
.
點(diǎn)評:本題是對一次函數(shù)的綜合考查,主要涉及聯(lián)立兩函數(shù)解析式求交點(diǎn)坐標(biāo),面積求解,求分段函數(shù)的解析式,二次函數(shù)的增減性,正確表示出函數(shù)的解析式是解題的關(guān)鍵.