5.导学号93774033当x=π/4时,函数f(x)=Asin(x+φ)(A>0)取得最小值,则函数y=f(3π/4 "-" x)(　　)

A.是奇函数且图像关于点(π/2 "," 0)对称

B.是偶函数且图像关于点(π,0)对称

C.是奇函数且图像关于直线x=π/2对称

D.是偶函数且图像关于直线x=π对称

解析∵当x=π/4时,函数f(x)取得最小值,

　　∴函数f(x)的图像关于直线x=π/4对称,

　　∴由f(0)=f(π/2)得φ=π/4+kπ,k∈Z,

　　∴f(x)=Asin(x+π/4+kπ),k∈Z,

　　∴f(3/4 π"-" x)=Asin(3π/4 "-" x+π/4+kπ)

　　=Asin(π-x+kπ)={■(Asinx"," k"为偶数," @"-" Asinx"," k"为奇数." )┤

　　∴y=f(3π/4 "-" x)是奇函数,且图像关于直线x=π/2对称.

答案C

6.已知关于x的方程√2sin(2x+π/4)=k在区间[0"," π/2]上有两个不同的实数解,则k的取值范围为　　　　　.

解析设f(x)=sin(2x+π/4).

　　∵x∈[0"," π/2],∴π/4≤2x+π/4≤5π/4.

　　易知函数f(x)=sin(2x+π/4)在[0"," π/8]上是增加的,在[π/8 "," π/2]上是减少的,

　　∴当方程sin(2x+π/4)=k/√2时,有f(0)≤k/√2

答案[1,√2)

7.已知函数f(x)=3sin(ωx"-" π/6)(ω>0)和g(x)=2cos(2x+φ)+1的图像的对称轴完全相同.若x∈[0"," π/2],则f(x)的取值范围是　　　　　.

解析由题意知ω=2,所以f(x)=3sin(2x"-" π/6).

　　因为x∈[0"," π/2],所以2x-π/6∈["-" π/6 "," 5π/6],

　　所以f(x)∈["-" 3/2 "," 3].

答案["-" 3/2 "," 3]

8.函数y=Asin(ωx+φ)("其中" A>0"," ω>0",|" φ"|" <π/2)的最大值是3,对称轴方程是x=π/6,要使函数的解析式为y=3sin(2x+π/6),还应给出的一个条件是　　　　　.(填上你认为正确的一个条件即可,不必考虑所有可能的情形)

解析若给出条件:周期T=π,则ω=2π/π=2,此时y=3sin(2x+φ).

　　由对称轴方程是x=π/6 知 π/6×2+φ=kπ+π/2(k∈Z).取k=0,得φ=π/6.

　　此时y=3sin(2x+π/6),符合题意.

答案答案不唯一,如周期T=π

9.导学号93774034将函数f(x)=sin ωx(其中ω>0)的图像向右平移π/4个单位长度,所得图像经过点(3π/4 "," 0),则ω的最小值是　　　　　.

解析将函数y=sin ωx(其中ω>0)的图像向右平移π/4个单位长度,所得图像对应的函数为y=sin ω(x"-" π/4).

再由所得图像经过点(3π/4 "," 0),