To determine which of the given relations do not represent functions, we need to recall the definition of a function. A relation is considered a function if every input (or first component of ordered pairs) is associated with exactly one output (or second component of ordered pairs).
Let's check each relation step-by-step:
1. Relation 1: [tex]\(\{(1, 2), (-2, 2), (5, 2), (4, 2)\}\)[/tex]
- Inputs: [tex]\(1, -2, 5, 4\)[/tex]
- Each input maps to a unique output.
- Conclusion: This relation is a function.
2. Relation 2: [tex]\(\{(7, 8), (7, 9), (7, 10), (7, 11)\}\)[/tex]
- Inputs: [tex]\(7, 7, 7, 7\)[/tex]
- The input [tex]\(7\)[/tex] maps to multiple outputs ([tex]\(8, 9, 10, 11\)[/tex]), which violates the definition of a function.
- Conclusion: This relation is not a function.
3. Relation 3: [tex]\(\{(0, 0)\}\)[/tex]
- Inputs: [tex]\(0\)[/tex]
- The input 0 maps to a single output 0.
- Conclusion: This relation is a function.
4. Relation 4: [tex]\(\{(1, 4), (-2, 8), (2, 2), (4, 9)\}\)[/tex]
- Inputs: [tex]\(1, -2, 2, 4\)[/tex]
- Each input maps to a unique output.
- Conclusion: This relation is a function.
After checking all the relations, we conclude that:
- Relation 1 is a function.
- Relation 2 is not a function.
- Relation 3 is a function.
- Relation 4 is a function.
Hence, the relation that does not represent a function is:
[tex]\[
\{(7, 8), (7, 9), (7, 10), (7, 11)\}
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{2}
\][/tex]
