Final answer:
The relation given is not a function because the input '5' maps to two different outputs, '3' and '4', which violates the definition of a function where each input must have only one output.
Step-by-step explanation:
To determine whether the given relation is a function, one must check if each input (or x-coordinate) maps to exactly one output (or y-coordinate). In the set of points given, which are (4, 9), (5, 3), (-2, 0), (5, 4), and (8, 1), we can see that the input '5' is associated with two different outputs: '3' and '4'. This violates the definition of a function which states that every input should correspond to only one output. Therefore, the relation is not a function.
A relation is a function if each input value (x) has only one corresponding output value (y). If any input has more than one output, then the relation is not a function.
In the given relation {(4, 9), (5, 3), (-2, 0), (5, 4), (8, 1)}, the input value 5 has two corresponding output values: 3 and 4. Therefore, the relation is not a function.