Question

已知函数f(x)=3sin(1/2-π/4),x∈R①用五点作图法画出函数f（x）在长度为一个周期的闭区间上的简图

②求此函数的对称中心和对称轴
已知函数f(x)=3sin(1/2x-π/4),x∈R①用五点作图法画出函数f（x）在长度为一个周期的闭区间上的简图②求此函数的对称中心和对称轴

Answer 1

f(x)=3sin(1/2x-π/4)

1.  列表：

1/2x-π/4        0            π/2             π               3π/2                2π

    x              π/2         3π/2          5π/2             7π/2               9π/2

 f(x)              0              3               0                  -3                   0

   描点成图

2

       由 1/2x-π/4=kπ+π/2  ==> 对称轴方程： x=2kπ+3π/2 k∈Z

      由 1/2x-π/4=kπ  ==>x=2kπ+π/2  对称中心（2kπ+π/2，0） k∈Z

Answer 2

没有x