What is a function's domain?

The domain of a function refers to the set of all possible input values, or x-values, for which the function is defined. This means that it specifies the range of values that can be substituted into the function without causing any mathematical issues, such as division by zero or taking the square root of a negative number.

Understanding the concept of a function's domain is fundamental in mathematics as it helps to identify valid inputs and understand the behavior of the function itself. For example, in a function defined as f(x) = 1/x, the domain would exclude x = 0, since dividing by zero is undefined. In contrast, the range of a function involves the output values (y-values) that result from the input values in the domain, which is a different concept altogether.

Thus, option A accurately defines the domain, and recognizing the significance of it enhances the overall comprehension of functions in mathematical contexts. The other options pertain to different aspects of functions, not specifically to their domains.