In this [previous post][1] I asked for the smallest set of continuous real functions that could generate Q by iteration starting from 0. Surprisingly one continuous function suffices.

In the question I gave the example of three rational functions that generate $\mathbb{Q}$, $f(x)=1/x$, $g(x)=x+1$ and  $h(x)=x-1$. It would be interesting to know if this is best possible and in particular whether one rational functional can generate all of $\mathbb{Q}$:

>Can $\mathbb{Q}$ be generate as the orbit of less than 3 rational functions?

The question [Orbits of rational functions][2] asks a more general question but I don't think  explicitly answers it for  $\mathbb{Q}$ itself.


  [1]: https://mathoverflow.net/q/412923/7113
  [2]: https://mathoverflow.net/q/280256/7113