Final answer:
The domain is (-∞, ∞) and the range is (-∞, ∞).
Step-by-step explanation:
The domain of a function refers to the set of all possible input values or x-values for which the function is defined. In this case, the function is defined for all real numbers, so the domain is (-∞, ∞).
The range of a function refers to the set of all possible output values or y-values that the function can take. For a linear function like f(x) = -4/3x - 12, the range is also all real numbers, so the range is (-∞, ∞).
The domain and range of a real-valued function can be determined by looking at the limitations placed on the variable x in the function, as well as the resulting f(x) values. For the given function f(x) = -4/3x - 12, there are no restrictions given in the problem statement, implying that x can take on any real value. Therefore, the domain of the function is all real numbers.
As for the range, since the function is linear, for all possible inputs of x, f(x) will yield all real numbers as well. Thus, the range is also all real numbers.
Therefore, the domain is (-∞, ∞) and the range is (-∞, ∞).