To determine the x-intercepts of the function given in the table, we need to identify the points where the function value [tex]\( f(x) \)[/tex] is equal to zero.
The table provides the following data points:
[tex]\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
-2 & 20 \\
\hline
-1 & 0 \\
\hline
0 & -6 \\
\hline
1 & -4 \\
\hline
2 & 0 \\
\hline
3 & 0 \\
\hline
\end{array}
\][/tex]
An x-intercept occurs when [tex]\( f(x) = 0 \)[/tex]. Let's examine the given data:
- At [tex]\( x = -2 \)[/tex], [tex]\( f(-2) = 20 \)[/tex], which is not zero.
- At [tex]\( x = -1 \)[/tex], [tex]\( f(-1) = 0 \)[/tex], which means [tex]\( (-1, 0) \)[/tex] is an x-intercept.
- At [tex]\( x = 0 \)[/tex], [tex]\( f(0) = -6 \)[/tex], which is not zero.
- At [tex]\( x = 1 \)[/tex], [tex]\( f(1) = -4 \)[/tex], which is not zero.
- At [tex]\( x = 2 \)[/tex], [tex]\( f(2) = 0 \)[/tex], which means [tex]\( (2, 0) \)[/tex] is an x-intercept.
- At [tex]\( x = 3 \)[/tex], [tex]\( f(3) = 0 \)[/tex], which means [tex]\( (3, 0) \)[/tex] is an x-intercept.
From the data, the x-intercepts are [tex]\( (-1, 0) \)[/tex], [tex]\( (2, 0) \)[/tex], and [tex]\( (3, 0) \)[/tex].
Among the given options, the x-intercept of the function is:
- [tex]\((-1, 0)\)[/tex]
Hence, the correct choice is [tex]\((-1, 0)\)[/tex].
