Final answer:
Option D. The domain and range of the function f(x) = 2x - 4 are both all real numbers, (-∞, ∞), since there are no restrictions on the values x can take and any real number can be outputted.
Step-by-step explanation:
The domain of a function refers to the set of all possible input values (x-values) for which the function is defined, and the range of a function is the set of all possible outputs (f(x) values) the function can produce. For the linear function f(x) = 2x - 4, the domain is all real numbers, since there are no restrictions on x; you can plug any real number into the equation and get a corresponding output. Therefore, the domain is (-∞, ∞). The range of this function is also all real numbers because as x takes on any value within the domain, the output can be any real number. Hence, the range is also (-∞, ∞).
The domain of the function f(x) = 2x - 4 represents all possible input values for the function. In this case, since there are no restrictions mentioned, the domain is all real numbers. Therefore, Option D is correct: Domain: x > 2.
The range of the function f(x) represents all possible output values. In this case, the function is a linear equation, so it will continue indefinitely in both the positive and negative directions. Therefore, the range is also all real numbers. Option D is correct: Range: (-[infinity], [infinity]).