To determine the [tex]\( x \)[/tex]-intercept of the function provided in the table, we need to identify the point where the function crosses the [tex]\( x \)[/tex]-axis. The [tex]\( x \)[/tex]-intercept of a function is the point where the output [tex]\( f(x) \)[/tex] equals zero, i.e., [tex]\( f(x) = 0 \)[/tex].
Based on the given data in the table:
[tex]\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
-2 & -10 \\
\hline
-1 & -8 \\
\hline
0 & -6 \\
\hline
1 & -4 \\
\hline
2 & -2 \\
\hline
3 & 0 \\
\hline
\end{array}
\][/tex]
We observe the function values at different points:
- When [tex]\( x = -2 \)[/tex], [tex]\( f(x) = -10 \)[/tex]
- When [tex]\( x = -1 \)[/tex], [tex]\( f(x) = -8 \)[/tex]
- When [tex]\( x = 0 \)[/tex], [tex]\( f(x) = -6 \)[/tex]
- When [tex]\( x = 1 \)[/tex], [tex]\( f(x) = -4 \)[/tex]
- When [tex]\( x = 2 \)[/tex], [tex]\( f(x) = -2 \)[/tex]
- When [tex]\( x = 3 \)[/tex], [tex]\( f(x) = 0 \)[/tex]
The [tex]\( x \)[/tex]-intercept is the point where [tex]\( f(x) \)[/tex] is zero. From the table, we can see that [tex]\( f(3) = 0 \)[/tex], which means the function crosses the [tex]\( x \)[/tex]-axis at the point [tex]\( (3, 0) \)[/tex].
Thus, the coordinate [tex]\((3,0)\)[/tex] is the [tex]\( x \)[/tex]-intercept of the function.
The correct answer is thus:
[tex]\( (3,0) \)[/tex]
