what is the domain of the relation shown below ( 4,2),(1,1),(0,0),(1,-1),(4,-2)

Look at the first element of each point:

{4, 1, 0, 1}   (do not write 4 twice, even tho' 4 shows up twice).

This is NOT a function, altho' it still is a relationship.  Why?   Because 4 shows up as an input twice.  In the case of a function, no input shows up more than once.