What is the definition of a function's domain?

The domain of a function is defined as the set of all possible input values, often represented by the variable x. This set includes every value that can be placed into the function without resulting in any contradictions or undefined situations, such as division by zero or the square root of a negative number in the realm of real numbers.

Understanding this definition is essential because it allows one to identify valid inputs for the function, ensuring proper usage in mathematical calculations and graphical representations. The values included in the domain can come from various types of numbers, depending on the function's formulation, such as integers, rational numbers, or real numbers.

The other options define different aspects of functions or do not accurately represent the concept of a domain. The outputs relate to the range, ordered pairs encompass both the domain and range, and maximum values pertain to specific characteristics of a function without addressing the overall set of inputs.