To determine which of the provided pairs of coordinates represents a function, we need to check if each input (x-value) corresponds to exactly one output (y-value). In other words, no x-value should be repeated with a different y-value for it to be considered a function.
Let's analyze the provided data pairs based on the responses you provided:
-
First set:
- (-5, 10)
- (-3, 5)
- (-3, 4)
- (0, 0)
- (5, -10)
Here, the x-value -3 is repeated with two different y-values (5 and 4), so this does not represent a function.
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Second set:
- (-12, 4)
- (-6, 10)
- (-4, 15)
- (-8, 18)
- (-12, 24)
The x-value -12 is repeated with different y-values (4 and 24), so this does not represent a function.
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Third set:
- (-8, -2)
- (-4, 1)
- (0, -2)
- (2, 3)
- (4, -4)
All x-values are unique, so this does represent a function.
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Fourth set:
- (-2, -3)
- (-1, -2)
- (0, -1)
- (0, 1)
- (1, 0)
The x-value 0 is repeated with two different y-values (-1 and 1), so this does not represent a function.
Based on this analysis, the only set that represents a function is the third set of coordinates.