Can this relation also be represented as {(-1, 1), (0, -2), (3, 1), (4, -1)}.?

In general, a relation can be represented by a set of ordered pairs (x,y), where x is a value in the domain of the relation and y is its corresponding value in the codomain.
Therefore, in our case, the relation is
[tex]\lbrace(0,-2),(3,1),(4,-1),(-1,-1)\rbrace[/tex]On the other hand, notice that (-1,1) is in the given set; that implies that the corresponding value of -1 in the codomain is 1 which is not true.