Final answer:
A relation is a function if each input has exactly one output. The vertical line test can determine if a graph represents a function, and an equation is a function if each independent variable value maps to only one dependent variable value. Economic models utilize functions to define relationships and graphs to visualize data.
Step-by-step explanation:
To determine if a relation represents a function, you need to check whether each input corresponds to exactly one output. For a graph, this is tested by using the vertical line test: if a vertical line intersects the graph in more than one point at any place, the graph does not represent a function. An equation represents a function if, for every value of the independent variable, there is only one possible value for the dependent variable.
In economic models, a function might define a relationship, like Professor = Adam Smith or Friends = Bob + Shawn + Margaret. When interpreting the equation of a line, you look at the slope and intercept to understand how changes in one variable affect another. Graphs, such as line graphs, pie charts, and bar graphs, illustrate different types of relationships between variables, showing trends, comparisons, and distributions effectively.