Final answer:
The domain is the set of all x-coordinates and the range is the set of all y-coordinates for a function given by ordered pairs, with the domain including the possible inputs for the function and the range consisting of the corresponding outputs. option A): Domain: Set of all x-coordinates, Range: Set of all y-coordinates.
Step-by-step explanation:
The domain and range are fundamental concepts in mathematics relating to functions. For a function represented by ordered pairs, such as those found in tabulated data or coordinates on a graph, the correct representation of the domain and range is found in option A): Domain: Set of all x-coordinates, Range: Set of all y-coordinates.
The domain consists of all the possible input values (x-values) for the function, which in turn produces output values, constituting the range (y-values). These sets can vary depending on the function in question. For example, if the domain of a variable X consists of university majors, it could be a list like {English, Mathematics, ...}, which is clearly not numerical. However, for a variable Y representing the number of classes taken, the domain could be numerical, such as {0, 1, 2, ...}. In summary, the domain can include various types of values, whereas the range includes the outcomes associated with each domain value.
Moreover, when we discuss discrete probability distributions or other functions in mathematics, it is important to understand these concepts to accurately interpret or graph the function. The domain and range provide constraints for what inputs can be used (domain) and what outputs can be expected (range).