1. **Problem statement:** We are given the function $$g(t) = \frac{t}{2}$$ and asked to determine where this function is continuous. 2. **Recall the continuity rule:** A function is continuous at a point if the limit of the function as it approaches that point equals the function's value at that point. 3. **Analyze the function:** The function $$g(t) = \frac{t}{2}$$ is a linear function, which means it is defined for all real numbers and has no breaks, jumps, or holes. 4. **Conclusion:** Since linear functions are continuous everywhere on the real number line, $$g(t)$$ is continuous for all real numbers. **Final answer:** The function $$g(t) = \frac{t}{2}$$ is continuous for all real numbers. Therefore, the correct choice is **a. all real numbers**.