If a function f is continuous on a closed interval [a,b], then the intermediate value theorem (IVT) states that f "hits" every "intermediate value" between f(a) and f(b). More precisely, if y lies (strictly) between f(a) and f(b), then there exists an input x lying (strictly) between a and b such that f(x) = y. The IVT can be useful in several geometric scenarios, such as root-finding for continuous functions (like polynomials).