Domain and range refer to what?

• A. Domain is the set of all possible input values; range is the set of all possible outputs.
• B. Domain is the set of all possible outputs; range is the set of all possible input values.
• C. Domain is the set of x-values of a circle; range is the set of y-values of a circle.
• D. Domain equals range.

Answer: (A)

When you think about a function, you can picture it as a rule that takes an input and gives an output. The domain is the set of all input values that you are allowed to feed into the rule. The range is the set of all outputs that the rule can produce from those inputs. This means domain answers “which x-values can we use?” and range answers “which y-values can result?”

For example, if a function is y = x^2 and you allow any real number as input, the domain is all real numbers, while the range is the nonnegative real numbers, since squaring any real input cannot produce a negative output. That shows why the statement describing domain as input values and range as output values is the best fit.

The other ideas don’t fit the general idea: domain isn’t the set of outputs, and range isn’t the set of inputs; and talking about x-values or y-values of a circle shifts from the general concept to a specific geometric object, which isn’t how domain and range are defined for functions. Domain and range aren’t always the same, so saying they are equal would only be true in special cases, not in general.