Question

What can you say about a function f defined on `RR`, periodic and growing ?

Answer 1

There is no such function.

Explanation:

Function `f` cannot be periodic and everywhere increasing.

If `f` is periodic, then for some `p > 0`, we have `f(x+p) = f(x)` for all `x`. But this implies that `f` is not strictly increasing on `[x,x+p]`