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

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

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Q. Which set of ordered pairs represents a function?\newline{(1,1),(5,4),(−4,−8),(−4,−5)} \{(1,1),(5,4),(-4,-8),(-4,-5)\} \newline{(2,−4),(−5,3),(−7,−6),(7,3)} \{(2,-4),(-5,3),(-7,-6),(7,3)\} \newline{(6,9),(1,1),(−9,−5),(6,5)} \{(6,9),(1,1),(-9,-5),(6,5)\} \newline{(−7,−9),(4,2),(−4,5),(−4,−6)} \{(-7,-9),(4,2),(-4,5),(-4,-6)\}
  1. Check for Function Definition: A set of ordered pairs represents a function if each input (first component of each ordered pair) corresponds to exactly one output (second component). We will check each set of ordered pairs to see if any input value is repeated with a different output value.
  2. First Set Analysis: For the first set {(1,1),(5,4),(−4,−8),(−4,−5)}\{(1,1),(5,4),(-4,-8),(-4,-5)\}, we see that the input value −4-4 is associated with two different output values, −8-8 and −5-5. This violates the definition of a function, so this set does not represent a function.
  3. Second Set Analysis: For the second set {(2,−4),(−5,3),(−7,−6),(7,3)}\{(2,-4),(-5,3),(-7,-6),(7,3)\}, each input value is unique and corresponds to exactly one output value. This set satisfies the definition of a function.
  4. Third Set Analysis: For the third set {(6,9),(1,1),(−9,−5),(6,5)}\{(6,9),(1,1),(-9,-5),(6,5)\}, we see that the input value 66 is associated with two different output values, 99 and 55. This violates the definition of a function, so this set does not represent a function.
  5. Fourth Set Analysis: For the fourth set {(−7,−9),(4,2),(−4,5),(−4,−6)}\{(-7,-9),(4,2),(-4,5),(-4,-6)\}, we see that the input value −4-4 is associated with two different output values, 55 and −6-6. This violates the definition of a function, so this set does not represent a function.
  6. Identify Correct Set: Since only the second set satisfies the definition of a function, it is the correct answer.

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