To determine if the given data represents a function, we need to understand the definition of a function in mathematics. A function is a relation where each input (x-coordinate) is associated with exactly one output (y-coordinate).
Given the points:
[tex]\( (2, -4), (2, 0), (2, 1), (2, 32) \)[/tex]
Let's analyze these points step-by-step:
1. List the input values (x-coordinates):
- From the given points, the x-coordinates are: [tex]\(2, 2, 2, 2\)[/tex].
2. Check the uniqueness of each input value:
- The input value for all the points given is [tex]\(2\)[/tex].
3. Determine if each input (x) is associated with only one output (y):
- In this dataset, the input value [tex]\(2\)[/tex] is associated with multiple outputs: [tex]\(-4, 0, 1, 32\)[/tex].
4. Conclusion:
- Since the input [tex]\(2\)[/tex] maps to multiple output values, this violates the definition of a function. A function requires that each input corresponds to exactly one output.
Based on this analysis, the given data does not satisfy the condition of having unique outputs for each input. Therefore, it is not a function.
Thus, the data represents a relation and not a function.
The answer is:
[tex]\[ \text{Relation} \][/tex]
