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Which set of ordered pairs does not represent a function?

{(-2,5),(6,-1),(-7,5),(-6,4)}

{(2,-4),(-7,9),(7,8),(3,8)}

{(3,-1),(3,7),(0,-3),(-4,-5)}

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

Which set of ordered pairs does not represent a function?\newline{(2,5),(6,1),(7,5),(6,4)} \{(-2,5),(6,-1),(-7,5),(-6,4)\} \newline{(2,4),(7,9),(7,8),(3,8)} \{(2,-4),(-7,9),(7,8),(3,8)\} \newline{(3,1),(3,7),(0,3),(4,5)} \{(3,-1),(3,7),(0,-3),(-4,-5)\} \newline{(8,5),(5,1),(1,5),(7,5)} \{(8,-5),(-5,-1),(1,-5),(-7,5)\}

Full solution

Q. Which set of ordered pairs does not represent a function?\newline{(2,5),(6,1),(7,5),(6,4)} \{(-2,5),(6,-1),(-7,5),(-6,4)\} \newline{(2,4),(7,9),(7,8),(3,8)} \{(2,-4),(-7,9),(7,8),(3,8)\} \newline{(3,1),(3,7),(0,3),(4,5)} \{(3,-1),(3,7),(0,-3),(-4,-5)\} \newline{(8,5),(5,1),(1,5),(7,5)} \{(8,-5),(-5,-1),(1,-5),(-7,5)\}
  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. Examine first set: Let's examine the first set: {(2,5),(6,1),(7,5),(6,4)}\{(-2,5),(6,-1),(-7,5),(-6,4)\}. We need to check if any xx-value is repeated with a different yy-value. (2,5)(-2,5) and (7,5)(-7,5) have different xx-values, so they are fine. (6,1)(6,-1) and (6,4)(-6,4) also have different xx-values. There are no repeated xx-values with different yy-values in this set.
  3. Examine second set: Now, let's examine the second set: (2,4),(7,9),(7,8),(3,8){(2,-4),(-7,9),(7,8),(3,8)}. Again, we check for repeated xx-values with different yy-values.\newline(2,4)(2,-4), (7,9)(-7,9), (7,8)(7,8), and (3,8)(3,8) all have unique xx-values. \newlineThere are no repeated xx-values with different yy-values in this set.
  4. Examine third set: Next, we examine the third set: {(3,1),(3,7),(0,3),(4,5)}\{(3,-1),(3,7),(0,-3),(-4,-5)\}. Here, we immediately see that the x-value 33 is repeated with different y-values: 1-1 and 77.(3,1)(3,-1) and (3,7)(3,7) indicate that the same x-value has two different y-values, which violates the definition of a function.
  5. Examine fourth set: Finally, let's examine the fourth set: (8,5),(5,1),(1,5),(7,5){(8,-5),(-5,-1),(1,-5),(-7,5)}. We check for repeated xx-values with different yy-values.(8,5)(8,-5), (5,1)(-5,-1), (1,5)(1,-5), and (7,5)(-7,5) all have unique xx-values. There are no repeated xx-values with different yy-values in this set.

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