To determine the y-intercept of the function given in the table, we need to find the point where [tex]\( x = 0 \)[/tex]. The y-intercept is the value of the function [tex]\( f(x) \)[/tex] when [tex]\( x \)[/tex] is zero.
Let's check the table for the value of [tex]\( f(x) \)[/tex] when [tex]\( x = 0 \)[/tex]:
[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]
From the table, when [tex]\( x = 0 \)[/tex], the function [tex]\( f(x) \)[/tex] evaluates to [tex]\( -6 \)[/tex]. Therefore, the y-intercept is the point [tex]\((0, -6)\)[/tex].
Let's cross-check this with the given options:
1. [tex]\( (0, -6) \)[/tex]
2. [tex]\( (-2, 0) \)[/tex]
3. [tex]\( (-6, 0) \)[/tex]
4. [tex]\( (0, -2) \)[/tex]
Clearly, the y-intercept of the continuous function is [tex]\((0, -6)\)[/tex].
