Question

How do you know if the mapping is a function

Answer 1

Suppose every object in the domain has only one image in the codomain, then the mapping is a function. Otherwise, it is not a functions

Looking at the given mapping:

-2 is mapped to both 1 and 3

0 is mapped to -3

1 is mapped to 4

3 is mapped to 1

Because -2 has more than one image, it disqualifies the mapping from being a function.