The relation {(4,10), (1,9), (5,10), (1,10)} is a function

it is not a function

for functions to work, there can only be one y value per x value aka if you see a set like this:  

{(4,2), (6,5), (10,1), (3,6), (6,7)}  

It is not a function because there are two y values (5 and 7) for one x value (6).