To determine the [tex]\( x \)[/tex]-intercept of the function [tex]\( f \)[/tex], we need to identify the [tex]\( x \)[/tex]-value for which the function [tex]\( f(x) \)[/tex] equals zero. This means we are looking for a row in the table where the value of [tex]\( f(x) \)[/tex] is 0.
Let's examine each row in the given table:
[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]
1. For [tex]\( x = -6 \)[/tex], [tex]\( f(x) = 4 \)[/tex] (not zero).
2. For [tex]\( x = -4 \)[/tex], [tex]\( f(x) = 0 \)[/tex] (this is zero).
3. For [tex]\( x = -2 \)[/tex], [tex]\( f(x) = -4 \)[/tex] (not zero).
4. For [tex]\( x = 0 \)[/tex], [tex]\( f(x) = -16 \)[/tex] (not zero).
5. For [tex]\( x = 1 \)[/tex], [tex]\( f(x) = -25 \)[/tex] (not zero).
From this analysis, we see that the row where [tex]\( f(x) \)[/tex] equals zero is:
[tex]\[
x = -4
\][/tex]
Therefore, the correct row in the table that reveals the [tex]\( x \)[/tex]-intercept of the function [tex]\( f \)[/tex] is:
[tex]\[
(-4, 0)
\][/tex]
So, the [tex]\( x \)[/tex]-intercept of the function [tex]\( f \)[/tex] is [tex]\( x = -4 \)[/tex].
