Salut/Hello!
Definition of a function: In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.
To make it more simple imagine a empty box with 2 holes ( one at the top and the other at the bottom ) and you insert a ball in the top hole and it falls thru the bottom hole.
When the ball falls inside the box (function) thru the top hole it'll be called
"input ball". The inside of the box can be called "function box:"
So once the ball falls out of the box thru the bottom hole it'll be called "output box(ball)".
Example: (using the image)
1. In this diagram of a function we have the domain X = {A,B,C} and codomain Y = {1,2,3} and it's defined with the set of ordered pairs {(A, 2), (B, 1), (C, 3)} and the set range is {A,B,C}
2. In this diagram of a function we have the domain A = {1,2,3} and codomain B = {X,Y,Z} and it's defined with the set of ordered pairs {(1, Y), (2, Y), (3, Z)} and the set range is {Y,Z}
3. In this diagram, representing the set of pairs {(1,D), (2,E), (2,F)} does not define a function because 2 is the first element in more than one ordered pair, but also because 3 is not the first element of any ordered pair.
Answer:
Relation 1: Function
Relation 2: Not a function (-8 is the first element in more than one ordered pair)
Relation 3: Function (a function can contain ordered pairs that include the same value for both the domain and codomain)
Relation 4: Not a function (5 is the first element in more than one ordered pair)
I hope it was helpful! :]