To determine the [tex]\( y \)[/tex]-intercept of a function [tex]\( f(x) \)[/tex], we need to find the value of the function when [tex]\( x = 0 \)[/tex]. This involves locating the row in the table where the [tex]\( x \)[/tex] value is zero and then reading the corresponding [tex]\( f(x) \)[/tex] value.
Here is the table provided:
[tex]\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
-1 & 2 \frac{2}{3} \\
\hline
0 & 2 \\
\hline
1 & 0 \\
\hline
2 & -6 \\
\hline
3 & -24 \\
\hline
\end{array}
\][/tex]
Let's examine each row to locate the row where [tex]\( x = 0 \)[/tex]:
- In the first row, [tex]\( x = -1 \)[/tex] and [tex]\( f(x) = 2 \frac{2}{3} \)[/tex].
- In the second row, [tex]\( x = 0 \)[/tex] and [tex]\( f(x) = 2 \)[/tex].
- In the third row, [tex]\( x = 1 \)[/tex] and [tex]\( f(x) = 0 \)[/tex].
- In the fourth row, [tex]\( x = 2 \)[/tex] and [tex]\( f(x) = -6 \)[/tex].
- In the fifth row, [tex]\( x = 3 \)[/tex] and [tex]\( f(x) = -24 \)[/tex].
The correct row in the table where [tex]\( x = 0 \)[/tex] is the second row. Correspondingly, the [tex]\( y \)[/tex]-intercept is the value of [tex]\( f(x) \)[/tex] at this row, which is [tex]\( 2 \)[/tex].
Thus, the row that reveals the [tex]\( y \)[/tex]-intercept of function [tex]\( f \)[/tex] is:
[tex]\[
\begin{array}{|c|c|}
\hline
0 & 2 \\
\hline
\end{array}
\][/tex]
