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

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

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Q. Which set of ordered pairs represents a function?\newline{(−9,2),(−9,0),(−4,8),(−3,4)} \{(-9,2),(-9,0),(-4,8),(-3,4)\} \newline{(3,−1),(9,−8),(4,4),(4,9)} \{(3,-1),(9,-8),(4,4),(4,9)\} \newline{(−2,−1),(7,−2),(−2,−3),(9,2)} \{(-2,-1),(7,-2),(-2,-3),(9,2)\} \newline{(−9,−3),(8,9),(5,−3),(6,−7)} \{(-9,-3),(8,9),(5,-3),(6,-7)\}
  1. Check for Function: 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 different output values.
  2. Set 11 Analysis: Examine the first set (−9,2),(−9,0),(−4,8),(−3,4){(-9,2),(-9,0),(-4,8),(-3,4)}. The input value −9-9 corresponds to two different output values, 22 and 00. This violates the definition of a function, so this set does not represent a function.
  3. Set 22 Analysis: Examine the second set (3,−1),(9,−8),(4,4),(4,9){(3,-1),(9,-8),(4,4),(4,9)}. The input value 44 corresponds to two different output values, 44 and 99. This also violates the definition of a function, so this set does not represent a function.
  4. Set 33 Analysis: Examine the third set (−2,−1),(7,−2),(−2,−3),(9,2){(-2,-1),(7,-2),(-2,-3),(9,2)}. The input value −2-2 corresponds to two different output values, −1-1 and −3-3. This again violates the definition of a function, so this set does not represent a function.
  5. Set 44 Analysis: Examine the fourth set {(−9,−3),(8,9),(5,−3),(6,−7)}\{(-9,-3),(8,9),(5,-3),(6,-7)\}. Each input value corresponds to exactly one output value. There are no repeated input values with different outputs. This set satisfies the definition of a function.
  6. Identify Function Set: Since the 4th4^{\text{th}} set is the only one where each input has a unique output, it is the set that represents a function.

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