Let's analyze the given table of values for the function [tex]\( f(x) \)[/tex]:
[tex]\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
-3 & 50 \\
\hline
-2 & 0 \\
\hline
-1 & -6 \\
\hline
0 & -4 \\
\hline
1 & -6 \\
\hline
2 & 0 \\
\hline
\end{array}
\][/tex]
First, we will determine the [tex]\( x \)[/tex]-intercepts. The [tex]\( x \)[/tex]-intercepts occur where the value of [tex]\( f(x) \)[/tex] is zero. By examining the table:
- When [tex]\( x = -2 \)[/tex], [tex]\( f(x) = 0 \)[/tex].
- When [tex]\( x = 2 \)[/tex], [tex]\( f(x) = 0 \)[/tex].
Therefore, the [tex]\( x \)[/tex]-intercepts shown in the table are [tex]\(-2\)[/tex] and [tex]\(2\)[/tex].
Next, we will determine the [tex]\( y \)[/tex]-intercept. The [tex]\( y \)[/tex]-intercept occurs where the value of [tex]\( x \)[/tex] is zero. By examining the table:
- When [tex]\( x = 0 \)[/tex], [tex]\( f(x) = -4 \)[/tex].
Therefore, the [tex]\( y \)[/tex]-intercept shown in the table is [tex]\(-4\)[/tex].
In conclusion:
- The [tex]\( x \)[/tex]-intercepts shown in the table are [tex]\(-2\)[/tex] and [tex]\(2\)[/tex].
- The [tex]\( y \)[/tex]-intercept shown in the table is [tex]\(-4\)[/tex].
So, we can complete the statements as follows:
- The [tex]\( x \)[/tex]-intercepts shown in the table are [tex]\(-2\)[/tex] and [tex]\(2\)[/tex].
- The [tex]\( y \)[/tex]-intercept shown in the table is [tex]\(-4\)[/tex].
