How to determine if a table has a function?

First determine the independent and dependent variables.
Once found, look down the column of independent variables,
1. if the values are all different, the table determines a function with the given independent variable.
2. if some values in the column of independent variables are identical, then look up the corresponding values of the dependent variables.  If the dependent variables are ALSO identical, we have a function.
3. if the corresponding values of dependent variables of identical independent variables are different, we do NOT have a function.

Examples: (x=independent variable, y=dependent variable)
Case 1: Function (values of x are all distinct (different))
x y
2 4
5 7
4 4

Case 2: Function (values of y are identical for those where x are identical)
x y
1 4
2 5
3 6
1 4  [(1,4) is identical to previous (1,4)]
4 7

Case 3: NOT a function (x identical, y not)
x y
1 3
2 4
3 5
4 6
1 7  [ (1,7) and (1,3) have conflicts.  when x=1, we don't know the value of y is 3 or 7]

Think of it as five or above give it a shove. change the 5 or above to the right to a zero and add one to the number on the left.