Which statement best distinguishes domain from range of a function?

• A. Domain is the set of y-values; Range is the set of x-values.
• B. Domain is the set of inputs; Range is the set of outputs.
• C. Domain describes rate of change; Range describes slope.
• D. Domain is the set of x-values; Range is the set of y-values.

Answer: (D)

The main idea is distinguishing inputs from outputs of a function. The domain is the set of x-values you can feed into the function (the inputs), and the range is the set of y-values you can get out (the outputs). Saying the domain is the set of x-values and the range is the set of y-values matches the standard way we describe functions as y = f(x), where x is the input and y is the output.

For example, if f(x) = sqrt(x), the domain is x ≥ 0 (the allowable inputs), and the range is y ≥ 0 (the resulting outputs). The wording that domain is the x-values and range is the y-values captures this input–output relationship precisely. Other options either swap the roles, describe something unrelated like rate of change, or are too vague about inputs and outputs.