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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, 5, comma, minus, 8, right parenthesis, comma, left parenthesis, 3, comma, 5, right parenthesis, comma, left parenthesis, 3, comma, minus, 3, right parenthesis, comma, left parenthesis, 2, comma, 8, right parenthesis, right curly bracket{(5,−8),(3,5),(3,−3),(2,8)}
left curly bracket, left parenthesis, minus, 6, comma, minus, 6, right parenthesis, comma, left parenthesis, 8, comma, 2, right parenthesis, comma, left parenthesis, 1, comma, minus, 6, right parenthesis, comma, left parenthesis, minus, 2, comma, minus, 2, right parenthesis, right curly bracket{(−6,−6),(8,2),(1,−6),(−2,−2)}
left curly bracket, left parenthesis, minus, 1, comma, minus, 3, right parenthesis, comma, left parenthesis, 0, comma, 2, right parenthesis, comma, left parenthesis, 4, comma, minus, 6, right parenthesis, comma, left parenthesis, minus, 2, comma, 2, right parenthesis, right curly bracket{(−1,−3),(0,2),(4,−6),(−2,2)}
left curly bracket, left parenthesis, 5, comma, minus, 4, right parenthesis, comma, left parenthesis, minus, 7, comma, minus, 1, right parenthesis, comma, left parenthesis, minus, 8, comma, 7, right parenthesis, comma, left parenthesis, minus, 5, comma, 4, right parenthesis, right curly bracket{(5,−4),(−7,−1),(−8,7),(−5,4)}

1 answer

To determine which set of ordered pairs does not represent a function, we need to remember the definition of a function. A function assigns exactly one output value (y-value) for each input value (x-value). This means that if any x-value appears more than once in the set of ordered pairs with different y-values, it is not a function.

Let's analyze the provided options:

  1. Set 1: \({(5,-8),(3,5),(3,-3),(2,8)}\)

    • x = 3 appears twice, with corresponding y-values of 5 and -3.
    • This does not represent a function.

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

    • All x-values (-6, 8, 1, -2) are unique.
    • This represents a function.

  3. Set 3: \({(-1,-3),(0,2),(4,-6),(-2,2)}\)

    • All x-values (-1, 0, 4, -2) are unique.
    • This represents a function.

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

    • All x-values (5, -7, -8, -5) are unique.
    • This represents a function.

Based on this analysis, the set that does not represent a function is:
Set 1: \({(5,-8),(3,5),(3,-3),(2,8)}\).