In front of you four statements that regard to functions f:R-->R.

1. Exist a>0 and exist x inRso that f(x+a)=f(x)

2. For every a>0, exist x inRso that f(x+a)=f(x)

3. Exist a>0 so that for every x inRso thatf(x+a)=f(x)

4. For every a>0 and every x inRso that f(x+a)=f(x)

Questions:

i. Characterize all functions from 1.

ii. Characterize all functions from 4.

iii. Find a function that is 1, but not 2,3,4

iv. Find a function that is 2, but not 3 and 4.

v. Find a function that is 3, but not 2 and 4.

Thanks!