Complexity of approximating a function value using queries


I am looking for information on problems of the following kind.

There is a function $ f: [0,1] \to \mathbb{R}$ that is continuous and monotonically-increasing, with $ f(0)<0$ and $ f(1)>0$ . You have to find the unique $ x\in[0,1]$ such that $ f(x)=0$ . You can access $ f$ only through queries of the type "what is $ f(x)$ ?". How many such queries do you need in order to approximate $ x$ up to some constant $ \epsilon$ ?

Here, the solution is simple: using binary search, the interval in which $ x$ can lie shrinks by 2 after each query, so $ \log_2(1/\epsilon)$ queries are sufficient. This is also an upper bound, since an adversary can always answer in such a way that the possible interval for $ x$ shrinks by at most 2 after each query.

However, one can think of more complicated problems of this kind, with several different functions and possibly different kinds of queries.

What is a term, and some references, for this kind of computational problems?