Final answer:
The set of points that represents a function is (3, 9), (-7, 1), (6, 12), (-3, -9), where each input is associated with exactly one output. The other sets listed violate the definition of a function because they show inputs paired with multiple outputs.
Step-by-step explanation:
In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. To determine which of the given sets of points represents a function, we must check for this particular property.
- (5, 1), (5, 2), (5, 3), (5, 4) - This set does not represent a function because the input '5' is related to more than one output (1, 2, 3, and 4).
- (-5, 6), (-5, 6), (-5, -6), (-5, -6) - This set does not represent a function because the input '-5' is related to different outputs, despite some points being repeated.
- (8, 3), (8, 3), (-8, -3), (-8, -3) - This set does not represent a function because it has repeating points, but this in itself does not violate the definition of a function.
- (3, 9), (-7, 1), (6, 12), (-3, -9) - This set represents a function because each input number corresponds to exactly one output number.
The correct choice is the set (3, 9), (-7, 1), (6, 12), (-3, -9), which is the fourth option.