1. **Problem:** Is the function $f(x) = \frac{4}{x - 3}$ continuous at $x = 3$? 2. **Step 1:** Recall the definition of continuity at a point $x = a$: A function $f$ is continuous at $a$ if $$\lim_{x \to a} f(x) = f(a).$$ 3. **Step 2:** Check if $f(3)$ is defined: $$f(3) = \frac{4}{3 - 3} = \frac{4}{0},$$ which is undefined. 4. **Step 3:** Since $f(3)$ is not defined, $f$ is not continuous at $x = 3$. **Final answer:** The function $f(x) = \frac{4}{x - 3}$ is not continuous at $x = 3$ because it is undefined there.