Black box of $f(x)$ means I can evaluate the polynomial $f(x)$ at any point.
Input: A black box of monic polynomial $f(x) \in\mathbb{S}[x]$ of degree $d$.
Question : $\mathbb{S} \subseteq \mathbb{Z}$, unbounded from both sides
Here $\mathbb{S} \subseteq \mathbb{Z} $ is an interval unbounded from both sides. For example interval $(-b,\infty]$, where $b$ is any fixed value and this interval is bounded from left side. I am allowed to make only constant many queries to oracle. I want to find such an subset $\mathbb{S}$.
Unbounded interval: An interval is said to be left-bounded or right-bounded if there is some real number that is, respectively, smaller than or larger than all its elements. An interval is said to be bounded if it is both left- and right-bounded; and is said to be unbounded otherwise
Please give a reference to material also if possible. If anything is not clear please ask in the comments I will try clear it.
Motivation : Find a polynomial in two or three queries