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Which set of ordered pairs represents a function? {(-1,6),(1,3),(1,-3),(-3,5)} {(9,-4),(2,-1),(8,-1),(9,1)} {(2,3),(2,-6),(-4,-4),(3,6)} {(-1,5),(0,-5),(8,5),(-7,2)}

Which set of ordered pairs represents a function?\newline{(−1,6),(1,3),(1,−3),(−3,5)} \{(-1,6),(1,3),(1,-3),(-3,5)\} \newline{(9,−4),(2,−1),(8,−1),(9,1)} \{(9,-4),(2,-1),(8,-1),(9,1)\} \newline{(2,3),(2,−6),(−4,−4),(3,6)} \{(2,3),(2,-6),(-4,-4),(3,6)\} \newline{(−1,5),(0,−5),(8,5),(−7,2)} \{(-1,5),(0,-5),(8,5),(-7,2)\}

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Q. Which set of ordered pairs represents a function?\newline{(−1,6),(1,3),(1,−3),(−3,5)} \{(-1,6),(1,3),(1,-3),(-3,5)\} \newline{(9,−4),(2,−1),(8,−1),(9,1)} \{(9,-4),(2,-1),(8,-1),(9,1)\} \newline{(2,3),(2,−6),(−4,−4),(3,6)} \{(2,3),(2,-6),(-4,-4),(3,6)\} \newline{(−1,5),(0,−5),(8,5),(−7,2)} \{(-1,5),(0,-5),(8,5),(-7,2)\}
  1. Check for Unique Inputs: A set of ordered pairs represents a function if each input (first element of each ordered pair) corresponds to exactly one output (second element of each ordered pair). We will check each set of ordered pairs to see if any input value is repeated with a different output value.
  2. Identify Violation of Function Definition: For the first set {(−1,6),(1,3),(1,−3),(−3,5)}\{(-1,6),(1,3),(1,-3),(-3,5)\}, we see that the input value 11 is associated with two different output values, 33 and −3-3. This violates the definition of a function.
  3. Identify Violation of Function Definition: For the second set {(9,−4),(2,−1),(8,−1),(9,1)}\{(9,-4),(2,-1),(8,-1),(9,1)\}, we see that the input value 99 is associated with two different output values, −4-4 and 11. This also violates the definition of a function.
  4. Identify Violation of Function Definition: For the third set {(2,3),(2,−6),(−4,−4),(3,6)}\{(2,3),(2,-6),(-4,-4),(3,6)\}, we see that the input value 22 is associated with two different output values, 33 and −6-6. This again violates the definition of a function.
  5. Identify Function Set: For the fourth set {(−1,5),(0,−5),(8,5),(−7,2)}\{(-1,5),(0,-5),(8,5),(-7,2)\}, we see that each input value is unique and is associated with only one output value. This set satisfies the definition of a function.
  6. Identify Function Set: For the fourth set {(−1,5),(0,−5),(8,5),(−7,2)}\{(-1,5),(0,-5),(8,5),(-7,2)\}, we see that each input value is unique and is associated with only one output value. This set satisfies the definition of a function. Since the fourth set is the only one where each input has a unique output, it represents a function.

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