  Let $f\in \mathbb{Q}(x)$ be a non-constant rational function. We consider
"Waring's Problem for $f(x)$," i.e., whether every element of $\bbq$ can be
written as a bounded sum of elements of $\{f(a)\mid a\in \mathbb{Q}\}$. For
rational functions of degree $2$, we give necessary and sufficient conditions.
For higher degrees, we prove that every polynomial of odd degree and every odd
Laurent polynomial satisfies Waring's Problem. We also consider the "Easier
Waring's Problem": whether every element of $\mathbb{Q}$ can be represented as
a bounded sum of elements of $\{\pm f(a)\mid a\in \mathbb{Q}\}$.
