下列函数中,周期为π,图像关于直线x=π/3对称的函数是（ ）A.y=2sin(x/2+π/3)B.y=2sin(x/2-π/3)C.y=2sin(2x+π/6)D.y=2sin(2x-π/3)答案上先用定义排除AB,周期为π,AB不成立.然后,又∵x=π/3为对称轴,由C项,我们可取点(0,-1/2)关于x=π/3的对称点(2π/3,-1/2),将x=2π/3代入C项,则y=-2≠-1/2.故选D项.疑问!Q:为什么取点(0,-1/2),C项中当x=0时y不应该=-1吗?

下列函数中,周期为π,图像关于直线x=π/3对称的函数是（ ）
A.y=2sin(x/2+π/3)
B.y=2sin(x/2-π/3)
C.y=2sin(2x+π/6)
D.y=2sin(2x-π/3)
答案上先用定义排除AB,周期为π,AB不成立.
然后,又∵x=π/3为对称轴,
由C项,我们可取点(0,-1/2)关于x=π/3的对称点(2π/3,-1/2),将x=2π/3代入C项,则y=-2≠-1/2.故选D项.
疑问!
Q:为什么取点(0,-1/2),C项中当x=0时y不应该=-1吗?