How can you tell whether data in a table represents a function?

Question

How can you tell whether data in a table represents a function? 

Answer 1

A function has an independent variable (often the variable x) and a dependent variable (often the variable y).  It is written as:

                      y = f(x)

 

For each value of x, there is at most one value of y.  That means there may be exactly one or else none.  So, if a single value of x in the table appears with two different values of y, then this is not a function.  When points are plotted (with the x-axis horizontal and the y-axis vertical), we have the "vertical line test": no two points may be on any vertical line.

 

Note that the possible values for the variable x are called the domain of the function and the possible values for the variable y are called the range of the function.