To determine if the given data represents a function, we need to verify if each element in the domain (set of x-values) maps to exactly one element in the range (set of y-values). In simpler terms, each input must have a unique output.
Let's go through the data step-by-step:
1. List the pairs:
We have the following pairs of [tex]\( (x, y) \)[/tex]:
- [tex]\( (-1, 0) \)[/tex]
- [tex]\( (8, 3) \)[/tex]
- [tex]\( (9, 9) \)[/tex]
2. Check for unique mappings:
- The x-value [tex]\(-1\)[/tex] maps to the y-value [tex]\(0\)[/tex].
- The x-value [tex]\(8\)[/tex] maps to the y-value [tex]\(3\)[/tex].
- The x-value [tex]\(9\)[/tex] maps to the y-value [tex]\(9\)[/tex].
3. Verify unique x-values:
- The x-value [tex]\(-1\)[/tex] is unique in the domain.
- The x-value [tex]\(8\)[/tex] is unique in the domain.
- The x-value [tex]\(9\)[/tex] is unique in the domain.
Since each x-value maps to exactly one unique y-value and there are no repeated x-values with different y-values, this mapping satisfies the definition of a function.
Therefore, the given data represents a function.
Answer: Yes
