Respuesta
If $f$ is continuous on $[a, b]$ and $k$ is between $f(a)$ and $f(b)$, there exists at least one $c \in (a, b)$ such that $f(c) = k$.
Explicación
If $f(a)$ and $f(b)$ have opposite signs ($f(a) \cdot f(b) < 0$), IVT guarantees at least one root $c \in (a, b)$ where $f(c) = 0$.