To find the value of [tex]\((p+q)(2)\)[/tex] using the given tables, we need to evaluate the expressions for both [tex]\(p(2)\)[/tex] and [tex]\(q(2)\)[/tex] and then add them together. Let's break this down step-by-step:
1. First, we look at the table for [tex]\(p(x)\)[/tex]. Locate the row where [tex]\(x = 2\)[/tex]:
[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $p(x)$ \\
\hline
4 & -1 \\
\hline
2 & 3 \\
\hline
-3 & 2 \\
\hline
\end{tabular}
\][/tex]
From this table, we see that [tex]\(p(2) = 3\)[/tex].
2. Next, we look at the table for [tex]\(q(x)\)[/tex]. Locate the row where [tex]\(x = 2\)[/tex]:
[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $q(x)$ \\
\hline
4 & 1 \\
\hline
2 & -2 \\
\hline
-3 & 5 \\
\hline
\end{tabular}
\][/tex]
From this table, we see that [tex]\(q(2) = -2\)[/tex].
3. Now, we simply add the values found in the previous steps:
[tex]\[
(p+q)(2) = p(2) + q(2) = 3 + (-2) = 1
\][/tex]
So, the value of [tex]\((p+q)(2)\)[/tex] is:
[tex]\[
(p+q)(2) = 1
\][/tex]
