The graph of the function f(x)=x+18sin(2πx), 0≤x≤1 is shown below. Define f1(x)=f(x),fn+1(x)=f(fn(x)), for n≥1.
Which of the following statements are true?
I. There are infinitely many x∈[0,1] for which limn→∞fn(x)=0.
II. There are infinitely many x∈[0,1] for which limn→∞fn(x)=12.
III. There are infinitely many x∈[0,1] for which limn→∞fn(x)=1.
IV. There are infinitely many x∈[0,1] for which limn→∞fn(x) does not exist.