Final answer:
The domain of a function is the set of all possible input values for which the function is defined. It could be a range of numbers, a list of categories, or any other set of potential inputs. Identifying the domain is essential in various mathematical applications.
Step-by-step explanation:
The domain of a function in mathematics is the complete set of possible values of the independent variable, or the input values for which the function is defined. Often, when dealing with real numbers, the domain is a range of values such as 0 ≤ x ≤ 20, meaning the function accepts any real number between 0 and 20, inclusive. It's important to identify the domain because it determines the set of possible inputs for the function.
For example, if we consider a function where X is a student's major, the domain of X would consist of all the majors offered at the university, plus 'undeclared'. Similarly, if Y represents the number of classes a student has taken in the previous semester, the domain of Y would be the set of all non-negative integers representing these class totals, potentially capped by the university's limit. Lastly, if Z denotes the amount of money spent on books in the previous semester, the domain of Z would include all amounts greater than or equal to zero, since one cannot spend a negative amount of money.
These examples help elucidate why understanding the domain is crucial in various applications, such as economic models, where defining functions and their relationships are essential.