To determine the row of the table that reveals the [tex]\( x \)[/tex]-intercept of the function [tex]\( f \)[/tex], we first need to understand what an [tex]\( x \)[/tex]-intercept is. The [tex]\( x \)[/tex]-intercept of a function [tex]\( f \)[/tex] is the point where the function crosses the [tex]\( x \)[/tex]-axis. This occurs where the value of the function [tex]\( f(x) \)[/tex] is zero.
We start by examining each row of the table to find the point where [tex]\( f(x) = 0 \)[/tex]:
[tex]\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
-6 & 4 \\
\hline
-4 & 0 \\
\hline
-2 & -4 \\
\hline
0 & -16 \\
\hline
1 & -25 \\
\hline
\end{array}
\][/tex]
We go through each value of [tex]\( f(x) \)[/tex]:
- For [tex]\( x = -6 \)[/tex], [tex]\( f(x) = 4 \)[/tex]. This does not intercept the [tex]\( x \)[/tex]-axis since [tex]\( f(x) \neq 0 \)[/tex].
- For [tex]\( x = -4 \)[/tex], [tex]\( f(x) = 0 \)[/tex]. This means that at [tex]\( x = -4 \)[/tex], the function crosses the [tex]\( x \)[/tex]-axis, so this is the [tex]\( x \)[/tex]-intercept.
- For [tex]\( x = -2 \)[/tex], [tex]\( f(x) = -4 \)[/tex]. This does not intercept the [tex]\( x \)[/tex]-axis since [tex]\( f(x) \neq 0 \)[/tex].
- For [tex]\( x = 0 \)[/tex], [tex]\( f(x) = -16 \)[/tex]. This does not intercept the [tex]\( x \)[/tex]-axis since [tex]\( f(x) \neq 0 \)[/tex].
- For [tex]\( x = 1 \)[/tex], [tex]\( f(x) = -25 \)[/tex]. This does not intercept the [tex]\( x \)[/tex]-axis since [tex]\( f(x) \neq 0 \)[/tex].
From our analysis, the row that reveals the [tex]\( x \)[/tex]-intercept of the function [tex]\( f \)[/tex] is the second row, where [tex]\( x = -4 \)[/tex] and [tex]\( f(x) = 0 \)[/tex].
Thus, the correct row of the table that reveals the [tex]\( x \)[/tex]-intercept of function [tex]\( f \)[/tex] is:
[tex]\[
\boxed{2}
\][/tex]
