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Which set of ordered pairs does not represent a function?

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Multiple Choice Answers
left curly bracket, left parenthesis, minus, 2, comma, 3, right parenthesis, comma, left parenthesis, 2, comma, minus, 9, right parenthesis, comma, left parenthesis, 9, comma, minus, 7, right parenthesis, comma, left parenthesis, minus, 2, comma, 9, right parenthesis, right curly bracket{(−2,3),(2,−9),(9,−7),(−2,9)}
left curly bracket, left parenthesis, minus, 9, comma, 8, right parenthesis, comma, left parenthesis, 5, comma, 8, right parenthesis, comma, left parenthesis, minus, 8, comma, 2, right parenthesis, comma, left parenthesis, minus, 1, comma, 6, right parenthesis, right curly bracket{(−9,8),(5,8),(−8,2),(−1,6)}
left curly bracket, left parenthesis, minus, 3, comma, minus, 4, right parenthesis, comma, left parenthesis, minus, 8, comma, 2, right parenthesis, comma, left parenthesis, minus, 5, comma, minus, 6, right parenthesis, comma, left parenthesis, 6, comma, 2, right parenthesis, right curly bracket{(−3,−4),(−8,2),(−5,−6),(6,2)}
left curly bracket, left parenthesis, 4, comma, 8, right parenthesis, comma, left parenthesis, minus, 7, comma, minus, 8, right parenthesis, comma, left parenthesis, minus, 8, comma, minus, 8, right parenthesis, comma, left parenthesis, minus, 1, comma, minus, 5, right parenthesis, right curly bracket{(4,8),(−7,−8),(−8,−8),(−1,−5)}

1 answer

A set of ordered pairs represents a function if each input (the first element of the pair) is associated with exactly one output (the second element of the pair).

Let's examine each set of ordered pairs:

  1. Set 1: {(-2, 3), (2, -9), (9, -7), (-2, 9)}

    • Here, -2 is paired with both 3 and 9. Since the input -2 has two different outputs, this set does not represent a function.

  2. Set 2: {(-9, 8), (5, 8), (-8, 2), (-1, 6)}

    • Each input is associated with exactly one output. This set does represent a function.

  3. Set 3: {(-3, -4), (-8, 2), (-5, -6), (6, 2)}

    • Each input is associated with exactly one output. This set does represent a function.

  4. Set 4: {(4, 8), (-7, -8), (-8, -8), (-1, -5)}

    • Each input is associated with exactly one output. This set does represent a function.

Conclusion: The first set {(-2, 3), (2, -9), (9, -7), (-2, 9)} does not represent a function because the input -2 is linked to two different outputs.