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Which set of ordered pairs does not represent a function?

{(9,2),(-5,2),(-4,0),(1,9)}

{(-3,-5),(0,8),(1,-2),(1,-9)}

{(-9,-5),(-5,4),(3,4),(-6,5)}

{(1,1),(-1,-8),(9,0),(6,0)}

Which set of ordered pairs does not represent a function?\newline{(9,2),(5,2),(4,0),(1,9)} \{(9,2),(-5,2),(-4,0),(1,9)\} \newline{(3,5),(0,8),(1,2),(1,9)} \{(-3,-5),(0,8),(1,-2),(1,-9)\} \newline{(9,5),(5,4),(3,4),(6,5)} \{(-9,-5),(-5,4),(3,4),(-6,5)\} \newline{(1,1),(1,8),(9,0),(6,0)} \{(1,1),(-1,-8),(9,0),(6,0)\}

Full solution

Q. Which set of ordered pairs does not represent a function?\newline{(9,2),(5,2),(4,0),(1,9)} \{(9,2),(-5,2),(-4,0),(1,9)\} \newline{(3,5),(0,8),(1,2),(1,9)} \{(-3,-5),(0,8),(1,-2),(1,-9)\} \newline{(9,5),(5,4),(3,4),(6,5)} \{(-9,-5),(-5,4),(3,4),(-6,5)\} \newline{(1,1),(1,8),(9,0),(6,0)} \{(1,1),(-1,-8),(9,0),(6,0)\}
  1. Define function as relation: A function is defined as a relation where each input ( extit{x}-value) has exactly one output ( extit{y}-value). To determine which set of ordered pairs does not represent a function, we need to check if there are any repeated extit{x}-values with different extit{y}-values in each set.
  2. Check first set: Check the first set: {(9,2),(5,2),(4,0),(1,9)}\{(9,2),(-5,2),(-4,0),(1,9)\}\newlineIn this set, all xx-values are unique. Therefore, this set represents a function.
  3. Check second set: Check the second set: {(3,5),(0,8),(1,2),(1,9)}\{(-3,-5),(0,8),(1,-2),(1,-9)\}\newlineIn this set, the x-value 11 appears twice with two different y-values (2(-2 and 9-9). This violates the definition of a function.
  4. Identify non-function set: Since we have found a set that does not represent a function, we do not need to check the remaining sets. The second set is the answer to the question prompt.

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