Final answer:
A function is a mathematical concept that assigns exactly one output to each input. The Vertical Line Test is used to determine if a graph represents a function, and no input in a function can relate to more than one output. Functions can be presented in various forms such as equations, graphs, and tables.
Step-by-step explanation:
A function is a special type of relation in mathematics that assigns exactly one output for each input. A classic way to determine if a relationship is a function is to use the Vertical Line Test. If a vertical line intersects a graph more than once at any point, then the graph does not represent a function. This is because a function can only have one output (y-value) for each input (x-value).
For example, the equation y = 2x + 3 is a function because for every x-value there is only one y-value obtained. This is unlike y = x², where x-values can have the same y-value, such as (2,4) and (-2,4), but each x-value still leads to a single y-value, thus it is also a function.
Moreover, functions can be represented in different forms such as equations, graphs, tables, or mappings. The critical aspect is that no input relates to more than one output. In economic models, understanding functions can help analyze and predict relationships between different economic factors.