# Smooth Functions A function (in algebra) is said to be smooth on its entire domain if: - Its **domain is all real numbers** and - **Its [[Derivative|derivative]] is [[Function Discontinuities|continuous]]** **If all derivatives of a function are also continuous then it is said that the function is said to be analytic**. All analytic functions are differentiable, but not all differentiable functions are analytic. A function can be smooth (or differentiable) on its whole domain, or a portion of its domain.