To determine the largest value of \( x \) that would make the given list of points not a function, we should first understand the definition of a function. A relation is considered a function if every input (or \( x \)-value) corresponds to exactly one output (or \( y \)-value).
Looking at the points provided in the list:
- \( ( , 15) \)
- \( (6, 22) \)
- \( (15, 24) \)
For the points to not represent a function, it is required that there are at least two points where the same \( x \)-value corresponds to different \( y \)-values.
From the points provided:
- The point \( ( , 15) \) is incomplete and cannot be analyzed without knowing its \( x \)-value.
- The point \( (6, 22) \) has \( x=6 \).
- The point \( (15, 24) \) has \( x=15 \).
Since we are looking for the largest \( x \) that would make these points not a function, we need to check if we can assign the blank \( x \)-value in the first point in such a way that it makes the overall list fail the function test.
If we assume that the first point \( (x_1, 15) \) has \( x_1 = 15 \), then we would have two points with \( x = 15 \):
- \( (15, 15) \)
- \( (15, 24) \)
This would mean both points have the same \( x \)-value of 15, but different \( y \)-values (15 and 24), making the relation not a function.
Thus, the largest value of \( x \) that could be assigned to the first point to make this list of points not a function is \( \boxed{15} \).