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Given the following table of values, determine the number of [tex]$x$[/tex]-intercepts for the function.

\begin{tabular}{|c|c|}
\hline [tex]$x$[/tex] & [tex]$y$[/tex] \\
\hline -4 & -0.906 \\
\hline -2 & -0.625 \\
\hline 0 & 0.5 \\
\hline 2 & 5 \\
\hline 4 & 23 \\
\hline
\end{tabular}

A. The function has no [tex]$x$[/tex]-intercepts.

B. The function has more than one [tex]$x$[/tex]-intercept.

C. The function has exactly one [tex]$x$[/tex]-intercept.

D. Not enough information to answer the question.



Answer :

GinnyAnswer
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

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