(l_n)(x) = exp(-x^2n), for any even integer n, defines a family of such functions.
(m_q,n)(x) = x^n / (q+x^n), for any even integer n and any positive real number q
Looking for something more exotic?
let n(x) be the function which equals 0.5 if x is rational, and 1.0 otherwise.
let o(x) be the function which gives the probability of two events both occurring if they are independent and have probabilities o(x/2) and o(2x).
(just for fun, could somebody find a closed-form solution for this last function, if there is one? does it make sense, or is it missing a necessary "base case"? one can tell that that o(0) = 1, but... can the rest be found uniquely?)
So, in response to the OP's question... pick your favorite.
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