To determine whether a given set of ordered pairs represents a function, we need to check if each input (x-value) is associated with exactly one output (y-value). In other words, for each unique x-value, there should be a unique y-value.
Given the set of ordered pairs:
[tex]\[
\begin{array}{l}
(8, 10) \\
(0, -10) \\
(11, -2)
\end{array}
\][/tex]
1. We first extract the x-values from each ordered pair:
- From [tex]\( (8, 10) \)[/tex], the x-value is [tex]\( 8 \)[/tex].
- From [tex]\( (0, -10) \)[/tex], the x-value is [tex]\( 0 \)[/tex].
- From [tex]\( (11, -2) \)[/tex], the x-value is [tex]\( 11 \)[/tex].
2. Next, we check if all the x-values are unique:
- The x-values are [tex]\( 8 \)[/tex], [tex]\( 0 \)[/tex], and [tex]\( 11 \)[/tex].
3. Since there are no repeated x-values, each x-value maps to only one corresponding y-value:
- [tex]\( 8 \)[/tex] maps to [tex]\( 10 \)[/tex]
- [tex]\( 0 \)[/tex] maps to [tex]\( -10 \)[/tex]
- [tex]\( 11 \)[/tex] maps to [tex]\( -2 \)[/tex]
Since each x-value is unique and corresponds to exactly one y-value, the relation is indeed a function.
Hence, the answer is:
[tex]\[
\boxed{\text{yes}}
\][/tex]
