Final answer:
The correct answer is B, where a relation is any set of ordered pairs and a function is a set of ordered pairs with unique x-values. Functions are important in economic models to represent relationships between variables.
Step-by-step explanation:
To address the student's question, the correct answer is B: A relation is any set of ordered pairs. A function is a set of ordered pairs in which no two different ordered pairs have the same first coordinate. This means that every x-value (or input) in a function must be associated with exactly one y-value (or output). However, a relation can include multiple pairs with the same first coordinate but different second coordinates.
For example, if we have a set of ordered pairs {(2, 3), (4, 5), (2, -1)}, this is a relation because it's simply a collection of pairs. However, it's not a function because the x-value 2 is associated with two different y-values (3 and -1). In economic models, functional relationships are crucial because they define how one variable changes in response to another, which is often critical to understanding the dynamics of economic systems. A common example of a function in economics is a linear equation, such as y = a + bx, which describes a linear relationship between two economic variables.