Hello there. To solve this question, we'll have to look at the diagram and find the ordered pairs of this relation and determine whether or not it is a function.
First, let's copy the diagram as follows:
First, the ordered pairs (x, y) can be found by taking the values of x from the input bubble and the y values from the output bubble, in the order they are connect by the arrows:
(10, 0), (20, 0), (30, 10), (40, 5)
Now, to determine if it is a function or not. We have to remember that there are three types of functions: injective, surjective and bijective.
The first happens when every element from the input is connected to only one element from the output (although we don't need that every value from the output have a pair)
The second happens when every value of the input is connected to an element from the output, but there aren't any elements left in the output set.
The latter happens when both of the above conditions are satisfied: every element from the output set have a pair and it is only one number from the input.
As you can see, there are two values that gives us the same result: (10, 0) and (20, 0)
This means that this cannot be a injective function.
But according to the second definition, this can be a surjective function, given that there are no values from the output without a pair and every element from the domain do as well.
Therefore, we say this relation is a function.