题目内容
已知函数![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103101841590313014/SYS201311031018415903130003_ST/0.png)
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103101841590313014/SYS201311031018415903130003_ST/1.png)
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103101841590313014/SYS201311031018415903130003_ST/2.png)
A.
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103101841590313014/SYS201311031018415903130003_ST/3.png)
B.y=2sin2
C.
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103101841590313014/SYS201311031018415903130003_ST/4.png)
D.y=2sin4
【答案】分析:函数f(x)=2sin(ωx-
),根据它的图象与x轴的两个相邻交点的距离等于
,求得ω=2.图象向左平移
个单位长度得到函数y=2sin[2(x+
)-
)]=2sin(2x)的图象,由此求得y=g(x)的解析式.
解答:解:∵函数
=2sin(ωx-
),根据它的图象与x轴的两个相邻交点的距离等于
,
可得
=
,∴ω=2.
将函数y=f(x)的图象向左平移
个单位长度得到函数y=2sin[2(x+
)-
)]=2sin(2x)的图象,
故y=g(x)的解析式是 y=2sin2x,
故选B.
点评:本题主要考查由函数y=Asin(ωx+∅)的部分图象求函数的解析式,函数y=Asin(ωx+∅)的图象变换,属于中档题.
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103101841590313014/SYS201311031018415903130003_DA/0.png)
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103101841590313014/SYS201311031018415903130003_DA/1.png)
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103101841590313014/SYS201311031018415903130003_DA/2.png)
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103101841590313014/SYS201311031018415903130003_DA/3.png)
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103101841590313014/SYS201311031018415903130003_DA/4.png)
解答:解:∵函数
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103101841590313014/SYS201311031018415903130003_DA/5.png)
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103101841590313014/SYS201311031018415903130003_DA/6.png)
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103101841590313014/SYS201311031018415903130003_DA/7.png)
可得
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103101841590313014/SYS201311031018415903130003_DA/8.png)
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103101841590313014/SYS201311031018415903130003_DA/9.png)
将函数y=f(x)的图象向左平移
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103101841590313014/SYS201311031018415903130003_DA/10.png)
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103101841590313014/SYS201311031018415903130003_DA/11.png)
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103101841590313014/SYS201311031018415903130003_DA/12.png)
故y=g(x)的解析式是 y=2sin2x,
故选B.
点评:本题主要考查由函数y=Asin(ωx+∅)的部分图象求函数的解析式,函数y=Asin(ωx+∅)的图象变换,属于中档题.
![](http://thumb2018.1010pic.com/images/loading.gif)
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