Question 970873

recall:  

A function is a set of ordered pairs in which each x-element has {{{only}}} {{{ONE}}} y-element associated with it.

 Vertical line test: each vertical line drawn through the graph will intersect a function in {{{only}}} {{{one}}} location 

a. {(5, 11), (6, 2), (3, 2), (4, 7), (1, 3)}
In the relation above the domain is {1,3,4, 5, 6 }
And the range is { 2, 3, 7,11 }

=> has (6, 2), (3, 2) where 2 different x-element have same y-element; but that is ok if relation {{{is}}} a function

b. {(1, 11), (6, 2), (3, 4), (5, 7), (8, 12)}

relation {{{is}}} a function

c. {(1, 11), (6, 2), (3, 4), (9, 7), (8, 12)}

relation {{{is}}} a function

d. {(1, 5), (6, 2), (3, 4), (5, 7), (6, 12)}

=> relation {{{is}}}{{{not}}} a function because  (6, 2)and (6, 12) have same x-element