In order to find out which of the following relation is a function, first, it is important to know that what exactly is a function?
A function is a relation in which every input is mapped to a single output.
If in case, there are two outputs for one input then it is not a function.
Let's analyze each of the given options.
Option A;
(0, 10), (-9, 3), (0, 9), (-9,-5)
As you can see in the above coordinates, the x = 0 has two different outputs y = 10 and y = 9
Similarly, x = -9 has two different outputs y = 3 and y = -5
Therefore, option A is not a function.
Option B:
(10,6), (3, -9), (9,0), (10,-5)
As you can see in the above coordinates, each input x has a single output y.
Therefore, option B is a function.
Option C:
(6, 10), (-9, 3), (0, 9), (-5, 10)
As you can see in the above coordinates, each input x has a single output y.
Therefore, option C is a function.
Option D:
(6, 10), (-9,3), (0, 9), (0, -5)
As you can see in the above coordinates, the x = 0 has two different outputs y = 9 and y = -5
Therefore, option D is not a function.