Final answer:
A function in math defines a unique output for each input, and is often used in economic models to describe relationships. On a graph, a function is represented by a line where each x-coordinate corresponds to one y-coordinate only. A non-function occurs when an input has multiple outputs, such as a vertical line on a graph.
Step-by-step explanation:
A function in math is a special type of relationship between values, where each input (often called an independent variable) is associated with exactly one output (often called a dependent variable). When we express economic models, functions help to represent these relationships. For instance, if we say 'Professor = Adam Smith', we're defining a relationship where the term 'Professor' functionally relates to 'Adam Smith'. Similarly, 'Friends = Bob + Shawn + Margaret' represents a summation of friends creating a group.
On a graph, a line can represent a function if for every input value (x-coordinate), there is only one output value (y-coordinate). This follows the mathematical form of a linear equation, for example, y = mx + b or y = a + bx, where m or b represents the slope of the line and b or a represents the y-intercept, respectively. However, if a graphed line is vertical, it means for some input x, there are multiple output y values, which violates the definition of a function.
Therefore, a non-function on a graph is a relation where an input has multiple outputs. An example of this would be a vertical line, which does not pass the vertical line test; if any vertical line intersects the graph in more than one point, the graph does not represent a function.