To determine the number of [tex]\( x \)[/tex]-intercepts from the given table, let's carefully analyze the data:
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-4 & -0.906 \\
\hline
-2 & -0.625 \\
\hline
0 & 0.5 \\
\hline
2 & 5 \\
\hline
4 & 23 \\
\hline
\end{array}
\][/tex]
An [tex]\( x \)[/tex]-intercept occurs where the value of [tex]\( y \)[/tex] is zero ([tex]\( y = 0 \)[/tex]). We need to check each pair [tex]\((x, y)\)[/tex] from the table to see if [tex]\( y \)[/tex] equals 0:
- For [tex]\( x = -4 \)[/tex], [tex]\( y = -0.906 \)[/tex]. (not zero)
- For [tex]\( x = -2 \)[/tex], [tex]\( y = -0.625 \)[/tex]. (not zero)
- For [tex]\( x = 0 \)[/tex], [tex]\( y = 0.5 \)[/tex]. (not zero)
- For [tex]\( x = 2 \)[/tex], [tex]\( y = 5 \)[/tex]. (not zero)
- For [tex]\( x = 4 \)[/tex], [tex]\( y = 23 \)[/tex]. (not zero)
From our evaluation, we see that none of the [tex]\( y \)[/tex] values in the given pairs is zero. Therefore, there are no points [tex]\((x, y)\)[/tex] in the table where [tex]\( y = 0 \)[/tex].
Based on this analysis, the correct answer is:
- A. the function has no [tex]\( x \)[/tex]-intercepts
