To determine which set of ordered pairs represents a function, we need to ensure that each input (or x-value) maps to exactly one output (or y-value). In other words, there should be no repeated x-values with different y-values in the set.
Let's examine each option step-by-step:
### Option A: [tex]\(\{(-8,-14),(-7,-12),(-6,-10),(-5,-8)\}\)[/tex]
- The x-values are: [tex]\(-8, -7, -6, -5\)[/tex]
- None of the x-values are repeated.
- Therefore, each x-value maps to a unique y-value.
- This set does represent a function.
### Option B: [tex]\(\{(-4,-14),(-9,-12),(-6,-10),(-9,-8)\}\)[/tex]
- The x-values are: [tex]\(-4, -9, -6, -9\)[/tex]
- The x-value [tex]\(-9\)[/tex] is repeated with different y-values: [tex]\(-12\)[/tex] and [tex]\(-8\)[/tex].
- Therefore, the set includes a repeated x-value with different y-values.
- This set does not represent a function.
### Option C: [tex]\(\{(8,-2),(9,-1),(10,2),(8,-10)\}\)[/tex]
- The x-values are: [tex]\(8, 9, 10, 8\)[/tex]
- The x-value [tex]\(8\)[/tex] is repeated with different y-values: [tex]\(-2\)[/tex] and [tex]\(-10\)[/tex].
- Therefore, the set includes a repeated x-value with different y-values.
- This set does not represent a function.
### Option D: [tex]\(\{(-8,-6),(-5,-3),(-2,0),(-2,3)\}\)[/tex]
- The x-values are: [tex]\(-8, -5, -2, -2\)[/tex]
- The x-value [tex]\(-2\)[/tex] is repeated with different y-values: [tex]\(0\)[/tex] and [tex]\(3\)[/tex].
- Therefore, the set includes a repeated x-value with different y-values.
- This set does not represent a function.
From the analysis, we see that:
- Only Option A has unique x-values and thus represents a function.
Therefore, the correct answer is:
[tex]\[
\boxed{A}
\][/tex]
