To determine which relation is a function, we need to apply the definition of a function. A relation is a function if every input (or [tex]\(x\)[/tex]-value) has exactly one output (or [tex]\(y\)[/tex]-value).
### Option A
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
4 & -7 \\
\hline
5 & -3 \\
\hline
5 & -2 \\
\hline
6 & 3 \\
\hline
7 & 6 \\
\hline
\end{array}
\][/tex]
In this table, we can see that the input [tex]\(x = 5\)[/tex] maps to two different outputs: [tex]\(y = -3\)[/tex] and [tex]\(y = -2\)[/tex]. According to the definition of a function, each input should have only one output. Hence, this relation is not a function.
### Option B
[tex]\(\{(-2,0),(-1,1),(0,2),(1,1),(2,0)\}\)[/tex]
Here, we need to check if each [tex]\(x\)[/tex]-value has a unique corresponding [tex]\(y\)[/tex]-value:
- For [tex]\(x = -2\)[/tex], the [tex]\(y\)[/tex]-value is [tex]\(0\)[/tex].
- For [tex]\(x = -1\)[/tex], the [tex]\(y\)[/tex]-value is [tex]\(1\)[/tex].
- For [tex]\(x = 0\)[/tex], the [tex]\(y\)[/tex]-value is [tex]\(2\)[/tex].
- For [tex]\(x = 1\)[/tex], the [tex]\(y\)[/tex]-value is [tex]\(1\)[/tex].
- For [tex]\(x = 2\)[/tex], the [tex]\(y\)[/tex]-value is [tex]\(0\)[/tex].
None of the [tex]\(x\)[/tex]-values repeats with different [tex]\(y\)[/tex]-values. Therefore, each input has a unique output. So this relation satisfies the conditions of being a function.
Given this analysis, the correct answer is:
[tex]\[
\boxed{2}
\][/tex]
