To find the [tex]\( y \)[/tex]-intercept of the function, we need to determine the point where the function intersects the [tex]\( y \)[/tex]-axis. This occurs when [tex]\( x = 0 \)[/tex].
Given the table:
[tex]\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
-4 & -10 \\
\hline
-3 & 0 \\
\hline
-2 & 0 \\
\hline
-1 & -4 \\
\hline
0 & -6 \\
\hline
1 & 0 \\
\hline
\end{array}
\][/tex]
We look at the value of [tex]\( f(x) \)[/tex] when [tex]\( x = 0 \)[/tex].
From the table, when [tex]\( x = 0 \)[/tex], [tex]\( f(x) = -6 \)[/tex].
Therefore, the [tex]\( y \)[/tex]-intercept of the continuous function in the table is at the point [tex]\((0, -6)\)[/tex].
Among the given options:
- [tex]\( (0, -6) \)[/tex]
- [tex]\( (-2, 0) \)[/tex]
- [tex]\( (-6, 0) \)[/tex]
- [tex]\( (0, -2) \)[/tex]
The correct [tex]\( y \)[/tex]-intercept is [tex]\((0, -6)\)[/tex].
