Final answer:
Option C, R = {(4, 5), (4, 8), (5, 10), (6, 12)}, is NOT a function because it has the same x-value (4) mapping to two different y-values (5 and 8), violating the definition of a function.
Step-by-step explanation:
To determine which of these relations is NOT a function, we need to remember that in a function, each input value should map to exactly one output value. That means, that for each x-value, there should be only one corresponding y-value.
- Option A: The set R = {(0, 0), (2, 6), (-4, -12), (-5, -15)} maps unique x-values to unique y-values, so it is a function.
- Option B: The set R = {(-2, 2), (2, -2), (-4, 4), (4, -4)} also shows a one-to-one relationship between x and y-values, and is a function.
- Option C: The set R = {(4, 5), (4, 8), (5, 10), (6, 12)} has the x-value 4 mapping to two different y-values, 5 and 8, which means it is NOT a function.
- Option D: The set R = {(2, 3), (4, 3), (6, 3), (5, 3)} has different x-values mapping to the same y-value, which is acceptable in a function.
Therefore, the relation that is NOT a function is Option C.