To determine which relation does not represent a function, we need to understand the definition of a function. A relation is a function if every element in the domain corresponds to exactly one element in the range. In simpler terms, no domain value (first element of the pair) should be repeated with a different range value (second element of the pair).
Let's examine each option step-by-step:
### Option A: {(3,0), (0, 3)}
- Domain elements: 3, 0
- Range elements: 0, 3
Every domain element is unique, meaning 3 and 0 do not repeat with different range values. Hence, this relation is a function.
### Option B: {(6,-2), (5,-2)}
- Domain elements: 6, 5
- Range elements: -2, -2
Every domain element is unique, meaning 6 and 5 do not repeat with different range values. Hence, this relation is a function.
### Option C: {(3, 4), (3, 5)}
- Domain elements: 3, 3
- Range elements: 4, 5
Here, the domain element 3 is repeated with different range values (4 and 5). This means that a single domain value (3) corresponds to more than one range value. Therefore, this relation is not a function.
### Option D: {(5, 5), (-5,-5)}
- Domain elements: 5, -5
- Range elements: 5, -5
Every domain element is unique, meaning 5 and -5 do not repeat with different range values. Hence, this relation is a function.
### Option E: {(1,-2), (-2, 1)}
- Domain elements: 1, -2
- Range elements: -2, 1
Every domain element is unique, meaning 1 and -2 do not repeat with different range values. Hence, this relation is a function.
Based on the examination, Option C is the relation that does not represent a function.
Therefore, the correct answer is:
Option C: {(3, 4), (3, 5)}
