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

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

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Full solution

Q. Which set of ordered pairs represents a function?\newline{(−3,−1),(−3,4),(3,6),(1,−6)} \{(-3,-1),(-3,4),(3,6),(1,-6)\} \newline{(2,−1),(−6,−3),(5,−6),(9,−3)} \{(2,-1),(-6,-3),(5,-6),(9,-3)\} \newline{(1,9),(5,−9),(−4,8),(−4,5)} \{(1,9),(5,-9),(-4,8),(-4,5)\} \newline{(−1,−7),(−1,−8),(6,2),(8,7)} \{(-1,-7),(-1,-8),(6,2),(8,7)\}
  1. Check for Function Definition: 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 is repeated with a different output.
  2. First Set Analysis: For the first set {(−3,−1),(−3,4),(3,6),(1,−6)}\{(-3,-1),(-3,4),(3,6),(1,-6)\}, the input −3-3 corresponds to two different outputs, −1-1 and 44. This violates the definition of a function.
  3. Second Set Analysis: For the second set {(2,−1),(−6,−3),(5,−6),(9,−3)}\{(2,-1),(-6,-3),(5,-6),(9,-3)\}, each input corresponds to exactly one output. There are no repeated inputs with different outputs. This set represents a function.
  4. Third Set Analysis: For the third set {(1,9),(5,−9),(−4,8),(−4,5)}\{(1,9),(5,-9),(-4,8),(-4,5)\}, the input −4-4 corresponds to two different outputs, 88 and 55. This violates the definition of a function.
  5. Fourth Set Analysis: For the fourth set {(−1,−7),(−1,−8),(6,2),(8,7)}\{(-1,-7),(-1,-8),(6,2),(8,7)\}, the input −1-1 corresponds to two different outputs, −7-7 and −8-8. This violates the definition of a function.
  6. Identify Function Set: Since only the second set has the property that each input corresponds to exactly one output, it is the only set that represents a function.

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