1. **Problem Statement:** We are given the function $$h(x) = 3x^2 + 5$$ and asked to determine where this function is continuous. 2. **Recall the continuity rule:** Polynomial functions, such as $$3x^2 + 5$$, are continuous everywhere on the real number line. This means there are no breaks, jumps, or holes in the graph of the function. 3. **Explanation:** Since $$h(x)$$ is a polynomial, it is continuous for all real values of $$x$$. There are no restrictions or points where the function is undefined. 4. **Conclusion:** The function $$h(x) = 3x^2 + 5$$ is continuous for all real numbers. **Final answer:** a. all real numbers