Question

Explain whether the table represents a function.

a) The table represents a function because each input has exactly one output assigned to it.
b) The table does not represent a function because there are positive inputs that have negative outputs, and there are negative inputs that have positive outputs.
c) The table represents a function because the inputs and outputs are integers.
d) The table does not represent a function because there are inputs that have more than one output assigned to them.

Answer 1

A table represents a function if each input has exactly one output. Positive or negative values or the data being integers are unrelated to the table being a function. The correct answer is that the table represents a function because each input corresponds to one output.

Step-by-step explanation:

To determine whether the table represents a function, we must evaluate the relationship between the inputs and outputs. A function requires that for every input, there is exactly one output associated with it. Having inputs with multiple outputs or the nature of the output values (positive or negative) doesn't affect whether it's a function or not.

Option d) correctly describes when a table does not represent a function, which is when an input has more than one output. This would violate the definition of a function. The examples of economic models using functions, such as Professor = Adam Smith or the export and import functions with horizontal lines, emphasize that functions describe relationships.

Lastly, the table provided with points (1,5), (2,10), (3,7), and (4,14) shows a different output for each input, which supports that the table does represent a function. The dependence of y on x is shown by these points, and they can be plotted on a graph to visualize the relationship.