1. **Problem Statement:** Determine whether the function $f(x) = 3x - 1$ is continuous at $x = 2$. 2. **Recall the definition of continuity at a point $x = c$:** A function $f$ is continuous at $x = c$ if: $$\lim_{x \to c} f(x) = f(c)$$ This means the limit of the function as $x$ approaches $c$ must exist and equal the function's value at $c$. 3. **Step 1: Compute $f(2)$:** $$f(2) = 3(2) - 1 = 6 - 1 = 5$$ 4. **Step 2: Evaluate the limit $\lim_{x \to 2} f(x)$:** Since $f(x) = 3x - 1$ is a polynomial (which is continuous everywhere), the limit is simply: $$\lim_{x \to 2} (3x - 1) = 3(2) - 1 = 5$$ 5. **Step 3: Compare the limit and the function value:** $$\lim_{x \to 2} f(x) = 5 = f(2)$$ Since they are equal, $f$ is continuous at $x = 2$. **Final answer:** The function $f(x) = 3x - 1$ is continuous at $x = 2$.