1. **Problem Statement:** Determine if the function $f(x)$ is continuous at a given point $x=a$. 2. **Definition of Continuity at a Point:** A function $f(x)$ is continuous at $x=a$ if the following three conditions are met: - $f(a)$ is defined. - The limit $\lim_{x \to a} f(x)$ exists. - The limit equals the function value: $\lim_{x \to a} f(x) = f(a)$. 3. **Formula and Explanation:** To check continuity, calculate: $$\lim_{x \to a^-} f(x), \quad \lim_{x \to a^+} f(x), \quad \text{and} \quad f(a)$$ If the left-hand limit and right-hand limit are equal and both equal $f(a)$, then $f$ is continuous at $a$. 4. **Intermediate Work:** - Evaluate $f(a)$. - Find $\lim_{x \to a^-} f(x)$ by approaching $a$ from the left. - Find $\lim_{x \to a^+} f(x)$ by approaching $a$ from the right. - Check if $\lim_{x \to a^-} f(x) = \lim_{x \to a^+} f(x) = f(a)$. 5. **Conclusion:** If all conditions hold, $f$ is continuous at $x=a$. Otherwise, $f$ is discontinuous at $x=a$. This method applies to any function and any point $a$ where continuity is questioned.