What does the domain of a function represent?

The domain of a function specifically represents the set of input values for which the function is defined. This means it includes all the possible values that can be substituted into the function without causing any mathematical inconsistencies, such as division by zero or taking the square root of a negative number when dealing with real numbers.

Understanding the domain is crucial because it determines the values that are permissible to input into the function. For example, if a function is defined as f(x) = 1/(x - 2), the domain would include all real numbers except for x = 2, as this would result in an undefined value.

In contrast, the other options refer to different aspects of a function. The set of output values refers to the range, coefficients pertain to the parameters of a polynomial function, and the range of possible function values describes the outputs derived from the inputs in the domain. Recognizing the definition of the domain helps clarify the inputs that yield valid outputs within the context of the function.