Function:
A function is a relationship in which there is one output for every input.
If there is more than one output for a single input then it is not a function.
Let us analyze each of the given ordered pairs.
The question asks which of the given options does not show a valid function.
Option A:
{(3, -2); (5, -3); (7, -4); (9, -5)}
As you can see, there is only one output for each input therefore, it is a valid function.
Option B:
{(3, -2); (6, -2); (9, -2); (12, -2)}
As you can see, all the inputs has the same output so, it is still a valid function.
Option C:
{(4, -2); (5, -3); (6, -4); (7, -5)}
As you can see, there is only one output for each input therefore, it is a valid function.
Option D:
{(4, -2); (5, -3); (4, -8); (5, -9)}
Notice that input 4 has two different outputs (-2 and -8) and also input 5 has two different outputs (-3 and -9)
Therefore, it is not a valid function.
Option D is the correct answer.