To find the x-intercept of the function [tex]\( f \)[/tex], we need to identify the point where [tex]\( f(x) = 0 \)[/tex]. In other words, we are looking for the row in the table where the second column (representing [tex]\( f(x) \)[/tex]) is equal to 0.
Let's examine the table row by row:
[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]
- In the first row, [tex]\( x = -6 \)[/tex] and [tex]\( f(x) = 4 \)[/tex]. Here, [tex]\( f(x) \neq 0 \)[/tex].
- In the second row, [tex]\( x = -4 \)[/tex] and [tex]\( f(x) = 0 \)[/tex]. Here, [tex]\( f(x) = 0 \)[/tex], which indicates the x-intercept.
- In the third row, [tex]\( x = -2 \)[/tex] and [tex]\( f(x) = -4 \)[/tex]. Here, [tex]\( f(x) \neq 0 \)[/tex].
- In the fourth row, [tex]\( x = 0 \)[/tex] and [tex]\( f(x) = -16 \)[/tex]. Here, [tex]\( f(x) \neq 0 \)[/tex].
- In the fifth row, [tex]\( x = 1 \)[/tex] and [tex]\( f(x) = -25 \)[/tex]. Here, [tex]\( f(x) \neq 0 \)[/tex].
From this examination, we can see that the x-intercept occurs in the second row. Therefore, the correct row number revealing the [tex]\( x \)[/tex]-intercept of the function [tex]\( f \)[/tex] is:
[tex]\[
\boxed{2}
\][/tex]
