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Which set of ordered pairs does not represent a function?

{(-6,7),(9,-1),(-1,-2),(-2,8)}

{(-2,9),(2,5),(-4,4),(6,9)}

{(8,8),(-7,-4),(9,5),(8,-6)}

{(-7,-5),(8,-1),(5,0),(4,-5)}

Which set of ordered pairs does not represent a function?\newline{(6,7),(9,1),(1,2),(2,8)} \{(-6,7),(9,-1),(-1,-2),(-2,8)\} \newline{(2,9),(2,5),(4,4),(6,9)} \{(-2,9),(2,5),(-4,4),(6,9)\} \newline{(8,8),(7,4),(9,5),(8,6)} \{(8,8),(-7,-4),(9,5),(8,-6)\} \newline{(7,5),(8,1),(5,0),(4,5)} \{(-7,-5),(8,-1),(5,0),(4,-5)\}

Full solution

Q. Which set of ordered pairs does not represent a function?\newline{(6,7),(9,1),(1,2),(2,8)} \{(-6,7),(9,-1),(-1,-2),(-2,8)\} \newline{(2,9),(2,5),(4,4),(6,9)} \{(-2,9),(2,5),(-4,4),(6,9)\} \newline{(8,8),(7,4),(9,5),(8,6)} \{(8,8),(-7,-4),(9,5),(8,-6)\} \newline{(7,5),(8,1),(5,0),(4,5)} \{(-7,-5),(8,-1),(5,0),(4,-5)\}
  1. Define Function Representation: A set of ordered pairs represents a function if each input ( extit{x}-value) is associated with exactly one output ( extit{y}-value). We need to check each set of ordered pairs to ensure that no extit{x}-value is repeated with different extit{y}-values.
  2. Check First Set: Check the first set: {(6,7),(9,1),(1,2),(2,8)}\{(-6,7),(9,-1),(-1,-2),(-2,8)\} Each xx-value is unique, so this set represents a function.
  3. Check Second Set: Check the second set: {(2,9),(2,5),(4,4),(6,9)}\{(-2,9),(2,5),(-4,4),(6,9)\} Each xx-value is unique, so this set also represents a function.
  4. Check Third Set: Check the third set: {(8,8),(7,4),(9,5),(8,6)}\{(8,8),(-7,-4),(9,5),(8,-6)\}\newlineThe xx-value 88 appears twice with different yy-values (88 and 6-6). This violates the definition of a function.
  5. Final Conclusion: Since the third set has a repeated xx-value with different yy-values, it does not represent a function. We do not need to check the fourth set because we have already found a set that does not represent a function.

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