Which term is the set of input values for which a function is defined?

Which term is the set of input values for which a function is defined?

• A. Range
• B. Codomain
• C. Image
• D. Domain

Answer: (D)

The main idea here is understanding what the domain of a function is. The domain is the set of all input values (the x-values) for which the function’s rule is defined and produces real outputs. For example, if you have a function defined by f(x) = sqrt(x − 2), you must have x − 2 ≥ 0, so x ≥ 2. The domain in this case is [2, ∞). Different terms describe other parts of the function. The codomain is the set where outputs could potentially live, regardless of whether every element actually occurs. The range is the actual set of outputs that the function produces from its domain, a subset of the codomain. The image is often used to refer to the outputs corresponding to a particular input set, and in many contexts is used synonymously with range. But the set of input values for which the function is defined—the domain—is the correct term.

The main idea here is understanding what the domain of a function is. The domain is the set of all input values (the x-values) for which the function’s rule is defined and produces real outputs. For example, if you have a function defined by f(x) = sqrt(x − 2), you must have x − 2 ≥ 0, so x ≥ 2. The domain in this case is [2, ∞).

Different terms describe other parts of the function. The codomain is the set where outputs could potentially live, regardless of whether every element actually occurs. The range is the actual set of outputs that the function produces from its domain, a subset of the codomain. The image is often used to refer to the outputs corresponding to a particular input set, and in many contexts is used synonymously with range. But the set of input values for which the function is defined—the domain—is the correct term.