To find the [tex]$x$[/tex]-intercepts of a continuous function, we need to identify the points where the function crosses the x-axis. These points occur where the function value, \( f(x) \), is equal to zero.
Looking at the table:
[tex]\[
\begin{tabular}{|c|c|}
\hline
[tex]$x$[/tex] & [tex]$f ( x )$[/tex] \\
\hline
-2 & 20 \\
\hline
-1 & 0 \\
\hline
0 & -6 \\
\hline
1 & -4 \\
\hline
2 & 0 \\
\hline
3 & 0 \\
\hline
\end{tabular}
\][/tex]
We observe the following pairs \((x, f(x))\):
- At \( x = -2 \), \( f(x) = 20 \)
- At \( x = -1 \), \( f(x) = 0 \)
- At \( x = 0 \), \( f(x) = -6 \)
- At \( x = 1 \), \( f(x) = -4 \)
- At \( x = 2 \), \( f(x) = 0 \)
- At \( x = 3 \), \( f(x) = 0 \)
To determine the [tex]$x$[/tex]-intercepts, we look for the rows where \( f(x) = 0 \):
- \( (-1, 0) \)
- \( (2, 0) \)
- \( (3, 0) \)
Therefore, the [tex]$x$[/tex]-intercepts of the function from the given points are:
\( (-1, 0) \), \( (2, 0) \), and \( (3, 0) \).
Among the options provided in the question, \( (-1, 0) \) is an [tex]$x$[/tex]-intercept.
Hence, the [tex]$x$[/tex]-intercept of the continuous function in the table is [tex]\( (-1, 0) \)[/tex].
