To determine the [tex]\( y \)[/tex]-intercept of the continuous function given in the table, we need to examine where the function crosses the [tex]\( y \)[/tex]-axis. The [tex]\( y \)[/tex]-intercept occurs where the [tex]\( x \)[/tex]-value is zero.
Here is the given table:
[tex]\[
\begin{tabular}{|c|c|}
\hline
x & f(x) \\
\hline
-4 & -10 \\
\hline
-3 & 0 \\
\hline
-2 & 0 \\
\hline
-1 & -4 \\
\hline
0 & -6 \\
\hline
1 & 0 \\
\hline
\end{tabular}
\][/tex]
From the table, we observe that the value of [tex]\( f(x) \)[/tex] when [tex]\( x = 0 \)[/tex] is -6.
As a result:
- The coordinates of the [tex]\( y \)[/tex]-intercept are [tex]\((0, -6)\)[/tex].
Thus, the [tex]\( y \)[/tex]-intercept of the continuous function in the table is [tex]\((0, -6)\)[/tex].
