1, and the period of the function f(x) is 2.

2. The image of the function f(x) is symmetrical about the straight line x= 1/3.

Find (1) and find the value of w, φ.

(2) Find the monotone increasing interval of function f(x)

(3) Draw the image of the function f(x) on [0,2] by list method.

(1) adopts the periodic formula:

T=2π/ω，

Get ω = π;

The image of the function f(x) is symmetrical about the straight line x= 1/3.

There is -φ/ω=x= 1/3.

Get φ=-π/3.

So f(x)=sin(πx-π/3).

(2)

F(x)=sin(πx-π/3)=- 1。

X=2k- 1/6，

X+T/2=2k+5/6，

Therefore, the monotonically increasing interval of the function f(x) is:

(2k- 1/6，2k+5/6)。 k∈Z。

(3) Draw the image of the function f(x) on [0,2] by list method.

As shown in the figure.