## University Calculus: Early Transcendentals (3rd Edition)

Take function $y=f(x)$ A function being right-continuous at a point $c$ means that - $c$ is in the domain of $f(x)$ ($f(c)$ exists) - $\lim_{x\to c^+}f(x)$ exists - $\lim_{x\to c^+}f(x)=f(c)$ A function being left-continuous at a point $c$ means that - $c$ is in the domain of $f(x)$ ($f(c)$ exists) - $\lim_{x\to c^-}f(x)$ exists - $\lim_{x\to c^-}f(x)=f(c)$ A function being continuous at a point $c$ must be both left-continuous and right-continuous at that point. In other words, $\lim_{x\to c^+}f(x)=\lim_{x\to c^-}f(x)=f(c)$