Which of the following defines the "domain" of a function?

The domain of a function is defined as the set of all allowable inputs for that function. This means that the domain includes all values that can be substituted into the function without resulting in any mathematical inconsistencies, such as division by zero or taking the square root of a negative number (in the context of real-valued functions).

Understanding the domain is crucial because it determines the potential values that can be used when evaluating the function. For example, if you have a function defined as ( f(x) = \sqrt{x} ), the domain is limited to all non-negative numbers since the square root of a negative number is not defined in the set of real numbers. Therefore, identifying the correct domain allows us to properly analyze and graph the function.

The other choices refer to aspects that are not representative of the domain. The set of all possible outputs describes the range of the function, the specific outputs for a given input pertain to what a function produces rather than what it accepts, and the average of all inputs is a statistical measure that does not define the function's inputs themselves.