To determine which set of ordered pairs represents a function, we need to check if each input (the first element of each pair) maps to exactly one output (the second element of the pair). In other words, no input can be repeated with a different output.
Let's analyze each option:
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{(2, –1), (8, 1), (–4, –1), (9, 1), (5, –1)}
- All inputs (2, 8, -4, 9, 5) are unique. This set represents a function.
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{(2, –2), (1, 5), (–2, 2), (1, –3), (8, –1)}
- The input '1' appears twice (1, 5) and (1, -3) with different outputs. This does not represent a function.
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{(–3, 1), (6, 3), (–3, 2), (–3, –3), (1, –1)}
- The input '–3' appears multiple times (–3, 1), (–3, 2), and (–3, –3) with different outputs. This does not represent a function.
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{(6, 8), (5, 2), (–2, –5), (1, –3), (–2, 9)}
- The input '–2' appears twice (–2, –5) and (–2, 9) with different outputs. This does not represent a function.
Thus, the only set of ordered pairs that represents a function is:
{(2, –1), (8, 1), (–4, –1), (9, 1), (5, –1)}.