To determine which table represents the inverse of the given function, we need to switch the roles of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] from the original table.
Given the original table:
[tex]\[
\begin{array}{|c|c|c|c|c|}
\hline
x & -2 & 0 & 2 & 4 \\
\hline
y & -1 & 5 & 11 & 17 \\
\hline
\end{array}
\][/tex]
The inverse table would switch [tex]\( x \)[/tex] and [tex]\( y \)[/tex]:
[tex]\[
\begin{array}{|c|c|c|c|c|}
\hline
x & -1 & 5 & 11 & 17 \\
\hline
y & -2 & 0 & 2 & 4 \\
\hline
\end{array}
\][/tex]
Comparing this with the given options:
Option A:
[tex]\[
\begin{array}{|c|c|c|c|c|}
\hline
x & -1 & 5 & 11 & 17 \\
\hline
y & -2 & 0 & 2 & 4 \\
\hline
\end{array}
\][/tex]
This matches our inverse table exactly.
Option B:
[tex]\[
\begin{array}{|c|c|c|c|c|}
\hline
x & -1 & 5 & 11 & 17 \\
\hline
y & 2 & 0 & -2 & -4 \\
\hline
\end{array}
\][/tex]
The [tex]\( y \)[/tex] values do not match the inverse table we calculated.
Option C:
[tex]\[
\begin{array}{|c|c|c|c|c|}
\hline
x & -2 & 0 & 2 & 4 \\
\hline
y & 1 & -5 & -11 & -17 \\
\hline
\end{array}
\][/tex]
Neither the [tex]\( x \)[/tex] nor the [tex]\( y \)[/tex] values match our inverse table.
Option D:
[tex]\[
\begin{array}{|c|c|c|c|c|}
\hline
x & -2 & 0 & 2 & 4 \\
\hline
y & 5 & 11 & 17 & 23 \\
\hline
\end{array}
\][/tex]
Again, neither the [tex]\( x \)[/tex] nor the [tex]\( y \)[/tex] values match our inverse table.
Therefore, the correct table that represents the inverse of the given function is:
Option A:
[tex]\[
\begin{array}{|c|c|c|c|c|}
\hline
x & -1 & 5 & 11 & 17 \\
\hline
y & -2 & 0 & 2 & 4 \\
\hline
\end{array}
\][/tex]
So, the correct answer is 1.
