To determine the [tex]\(x\)[/tex]-intercept of the continuous function represented by the given table, we need to identify the point where the function [tex]\(f(x)\)[/tex] crosses the x-axis. The [tex]\(x\)[/tex]-intercept occurs when [tex]\(f(x) = 0\)[/tex].
Examining the table:
[tex]\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
-1 & -9 \\
\hline
0 & -8 \\
\hline
1 & -7 \\
\hline
2 & 0 \\
\hline
3 & 19 \\
\hline
4 & 56 \\
\hline
\end{array}
\][/tex]
We see that at [tex]\(x = 2\)[/tex], [tex]\(f(x) = 0\)[/tex]. This means the function crosses the x-axis at the point [tex]\((2, 0)\)[/tex].
Therefore, the [tex]\(x\)[/tex]-intercept of the function is [tex]\((2, 0)\)[/tex].
