> [!Definition] Definition (Real-valued function of a single real variable) > A [[Function|function]] $f:U\to \mathbb{R}$ such that $U\subseteq \mathbb{R}$. > [!info] Vertical line test > A relation on $\mathbb{R}$ is a function iff passes the vertical line test - all vertical lines intersect a curve at most once then the curve represents a function. ^5342bc >See generalisations [[Real-Valued Function on Real n-Space (Multivariable Function)]] & [[Vector-Valued Function of Real variable]] & [[Vector Valued Function of Several Real Variables]]. # Properties - [[Limit of Real Function at a Point]]. - [[Continuous Real Function]]. - [[Fréchet Differentiation]]. - [[Riemann integration]].