To find the [tex]\( y \)[/tex]-intercept of the continuous function presented in the table, we need to identify the value of the function when [tex]\( x = 0 \)[/tex]. This is because the [tex]\( y \)[/tex]-intercept is the point where the graph of the function crosses the [tex]\( y \)[/tex]-axis.
Let's look at the table of values provided:
[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $f(x)$ \\
\hline
-2 & 15 \\
\hline
-1 & 10 \\
\hline
0 & 5 \\
\hline
1 & 0 \\
\hline
2 & -5 \\
\hline
3 & -10 \\
\hline
\end{tabular}
\][/tex]
From the table, we see that when [tex]\( x = 0 \)[/tex], the value of [tex]\( f(x) \)[/tex] (or [tex]\( y \)[/tex]) is 5. Therefore, the coordinates of the [tex]\( y \)[/tex]-intercept are [tex]\((0, 5)\)[/tex].
This corresponds to the point [tex]\((0, 5)\)[/tex] in the list of possible answers.
Thus, the correct answer is:
[tex]\[
\boxed{(0,5)}
\][/tex]
