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)}
Q. 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)}
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.
Check First Set: Check the first set: {(−6,7),(9,−1),(−1,−2),(−2,8)} Each x-value is unique, so this set represents a function.
Check Second Set: Check the second set: {(−2,9),(2,5),(−4,4),(6,9)} Each x-value is unique, so this set also represents a function.
Check Third Set: Check the third set: {(8,8),(−7,−4),(9,5),(8,−6)}The x-value 8 appears twice with different y-values (8 and −6). This violates the definition of a function.
Final Conclusion: Since the third set has a repeated x-value with different y-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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