To determine which table represents a function, we need to check whether each input (x-value) corresponds to exactly one output (y-value). In other words, for every unique x-value, there should be only one y-value associated with it.
Let's analyze each table:
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First table:
x y 2 1 2 6 2 8 2 9
- For x = 2, there are multiple y-values (1, 6, 8, 9). This is NOT a function.
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Second table:
x y -2 5 0 5 2 5 4 5
- All x-values are unique (-2, 0, 2, 4), each has a single y-value (5). This IS a function.
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Third table:
x y 5 1 -1 0 6 8 5 7
- For x = 5, there are two y-values (1, 7). This is NOT a function.
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Fourth table:
x y 5 0 3 3 3 1 8 7
- For x = 3, there are two y-values (3, 1). This is NOT a function.
Based on the analysis, the second table is the only one that represents a function.