In front of you four statements that regard to functions f:R-->R.
1. Exist a>0 and exist x in R so that f(x+a)=f(x)
2. For every a>0, exist x in R so that f(x+a)=f(x)
3. Exist a>0 so that for every x in R so thatf(x+a)=f(x)
4. For every a>0 and every x in R so 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!