Final answer:
The domain of the function is all real numbers and the range is also all real numbers.
Step-by-step explanation:
The domain of a function is the set of all possible input values (x-values) for which the function is defined. In this case, the function f(x) = 3x + 6 is defined for all real numbers. Therefore, the domain is the set of all real numbers.
The range of a function is the set of all possible output values (y-values) that the function can produce. Since f(x) = 3x + 6 is a linear function, its range is also the set of all real numbers.