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Which set of ordered pairs does not represent a function?

{(-3,5),(-4,2),(-8,-1),(-6,5)}

{(-8,3),(9,4),(8,1),(3,-2)}

{(5,9),(3,-9),(-5,3),(3,-8)}

{(9,-8),(-3,3),(-6,-3),(1,-8)}

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

Full solution

Q. Which set of ordered pairs does not represent a function?\newline{(3,5),(4,2),(8,1),(6,5)} \{(-3,5),(-4,2),(-8,-1),(-6,5)\} \newline{(8,3),(9,4),(8,1),(3,2)} \{(-8,3),(9,4),(8,1),(3,-2)\} \newline{(5,9),(3,9),(5,3),(3,8)} \{(5,9),(3,-9),(-5,3),(3,-8)\} \newline{(9,8),(3,3),(6,3),(1,8)} \{(9,-8),(-3,3),(-6,-3),(1,-8)\}
  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: Let's examine the first set: {(3,5),(4,2),(8,1),(6,5)}\{(-3,5),(-4,2),(-8,-1),(-6,5)\}. We need to check if any xx-value is repeated with a different yy-value.
  3. Check second set: In the first set, all xx-values are unique: 3-3, 4-4, 8-8, and 6-6. Since there are no repeated xx-values, this set represents a function.
  4. Check third set: Now, let's examine the second set: {(8,3),(9,4),(8,1),(3,2)}\{(-8,3),(9,4),(8,1),(3,-2)\}. Again, we check for any repeated xx-values with different yy-values.
  5. Final decision: In the second set, all xx-values are unique: 8-8, 99, 88, and 33. Since there are no repeated xx-values, this set also represents a function.
  6. Final decision: In the second set, all xx-values are unique: 8-8, 99, 88, and 33. Since there are no repeated xx-values, this set also represents a function.Next, let's examine the third set: {(5,9),(3,9),(5,3),(3,8)}\{(5,9),(3,-9),(-5,3),(3,-8)\}. We look for any repeated xx-values with different yy-values.
  7. Final decision: In the second set, all xx-values are unique: 8-8, 99, 88, and 33. Since there are no repeated xx-values, this set also represents a function.Next, let's examine the third set: {(5,9),(3,9),(5,3),(3,8)}\{(5,9),(3,-9),(-5,3),(3,-8)\}. We look for any repeated xx-values with different yy-values.In the third set, the xx-value 33 is repeated with different yy-values: 8-822 and 8-833. This means that for the same input, there are two different outputs, which violates the definition of a function.
  8. Final decision: In the second set, all xx-values are unique: 8-8, 99, 88, and 33. Since there are no repeated xx-values, this set also represents a function.Next, let's examine the third set: {(5,9),(3,9),(5,3),(3,8)}\{(5,9),(3,-9),(-5,3),(3,-8)\}. We look for any repeated xx-values with different yy-values.In the third set, the xx-value 33 is repeated with different yy-values: 8-822 and 8-833. This means that for the same input, there are two different outputs, which violates the definition of a function.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, as we have already found the set that does not represent a function.

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