What is the period of the function f(x) shown in the graph?

For this case what you should see is when the value "y" of any point of the graph is repeated again.
 In this case we have that the period will be given by:
 T = ((3/4) pi) - ((- 1/4) pi)
 T = ((3/4) pi) + ((1/4) pi)
 T = ((3 + 1/4) pi)
 T = ((4/4) pi)
 T = pi
 
 the period of the function f(x) shown in the graph is
 T = pi

Hi hello hello there is a good call from you i wanna was a really nice night and i’m gonna is your life day and you