Final answer:
To determine if f(x) is continuous at x = 3, check if the left-hand limit and right-hand limit are equal.
Step-by-step explanation:
To determine whether the function f(x) is continuous at x = 3, we need to check if the left-hand limit and the right-hand limit of the function at x = 3 exist and are equal.
For the left-hand limit, we substitute x = 3 into the first part of the function: 3(3) + 6 = 15.
For the right-hand limit, we substitute x = 3 into the second part of the function: 10(3) + 3 = 33.
Since the left-hand limit (15) is not equal to the right-hand limit (33), the function f(x) is not continuous at x = 3.