## Calculus (3rd Edition)

(a) If $f$ is left-continuous at $x=3$, then $\lim\limits_{x \to 3^{-}}f(x)=f(3)$. As $f(x)=2$ for $x\lt3,$ $\lim\limits_{x \to 3^{-}}f(x)=2$ $\implies f(3)=2$ (b) If $f$ is right-continuous at $x=3$, then $\lim\limits_{x \to 3^{+}}f(x)=f(3)$. As $f(x)=-4$ for $x\gt3,$ $\lim\limits_{x \to 3^{+}}f(x)=-4$ $\implies f(3)=-4$