Answer
The conditions are detailed in the Work step-by-step.
Work Step by Step
Take the function $y=f(x)$.
1) For an interior point $x=c$ in the interval:
$f$ is continuous at $x=c$ if three following conditions are satisfied:
- $f(c)$ exists ($c$ lies in the domain of $f$)
- $\lim_{x\to c}f(x)$ exists
- $\lim_{x\to c}f(x)=f(c)$
2) For endpoints $x=c$:
$f$ is continuous at $x=c$ if three following conditions are satisfied:
- $f(c)$ exists ($c$ lies in the domain of $f$)
- $\lim_{x\to c^+}f(x)$ exists (if $x=c$ is the left endpoint) or $\lim_{x\to c^-}f(x)$ exists (if $x=c$ is the right endpoint)
- $\lim_{x\to c^+}f(x)=f(c)$ (if $x=c$ is the left endpoint) or $\lim_{x\to c^-}f(x)=f(c)$ (if $x=c$ is the right endpoint)
