Final answer:
The domain of the function f(x) = 2/3x + 3 is all real numbers, as there are no restrictions on the values x can take. The provided answer choices do not match this correct domain.
Step-by-step explanation:
To find the domain of the function f(x) = ⅓x + 3, we need to consider the values of x that can be plugged into the function without causing any mathematical errors such as division by zero or taking the square root of a negative number. Inspection of this function reveals that there are no such restrictions—the function is a simple linear function with a slope of ⅓ and a y-intercept at 3. Therefore, all real numbers are valid inputs, making the domain all real numbers.
Range, on the other hand, refers to the possible outputs of the function, which in the given function, can also be any real number because a linear function continues infinitely in both directions. Since the range given in the question (-3, 0, 5, 9) is just a set of specific outputs and does not restrict the domain, they are not relevant to finding the domain.
Consequently, the correct choice for the domain of the function is: All real numbers which would typically be represented as (-∞, +∞) in interval notation, suggesting that none of the provided answer choices (A, B, C, or D) is correct.