1. **Problem:** Determine whether the function $f(x) = 3x^2 - 2x + 5$ is continuous at $x = 2$. 2. **Recall the definition of continuity at a point:** A function $f$ is continuous at $x = a$ if: $$\lim_{x \to a} f(x) = f(a)$$ This means the limit of the function as $x$ approaches $a$ must exist and be equal to the function's value at $a$. 3. **Evaluate $f(2)$:** $$f(2) = 3(2)^2 - 2(2) + 5 = 3 \times 4 - 4 + 5 = 12 - 4 + 5 = 13$$ 4. **Evaluate the limit $\lim_{x \to 2} f(x)$:** Since $f(x)$ is a polynomial, it is continuous everywhere, so the limit is simply the value at $x=2$: $$\lim_{x \to 2} f(x) = f(2) = 13$$ 5. **Conclusion:** Since the limit equals the function value at $x=2$, $f$ is continuous at $x=2$. \boxed{\text{The function } f(x) = 3x^2 - 2x + 5 \text{ is continuous at } x=2.}