Answer
The answer is detailed below.
Work Step by Step
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, $\lim_{x\to c^+}f(x)=\lim_{x\to c^-}f(x)=f(c)$
