To determine which ordered pairs are found on the graph of the inverse function, we need to understand that for an inverse function, the coordinates [tex]\((x, y)\)[/tex] of the original function [tex]\( f(x) \)[/tex] will be swapped to [tex]\((y, x)\)[/tex] on the graph of the inverse function [tex]\( f^{-1}(x) \)[/tex].
Given the table of values:
[tex]\[
\begin{array}{|c|c|}
\hline x & f(x) \\
\hline
-2 & 14 \\
\hline
-1 & 10 \\
\hline
0 & 6 \\
\hline
1 & 2 \\
\hline
2 & -2 \\
\hline
\end{array}
\][/tex]
We convert each [tex]\((x, f(x))\)[/tex] pair to [tex]\((f(x), x)\)[/tex].
Thus, the pairs for the inverse function are:
[tex]\[
(14, -2), (10, -1), (6, 0), (2, 1), (-2, 2)
\][/tex]
Now, we compare these reversed pairs with each given choice:
Choice A:
[tex]\((2, -14), (1, -10), (0, -6), (-1, -2), (-2, 2)\)[/tex]
These do not match our expected pairs.
Choice B:
[tex]\((-14, 2), (-10, 1), (-6, 0), (-2, -1), (2, -2)\)[/tex]
These do not match our expected pairs.
Choice C:
[tex]\((14, -2), (10, -1), (6, 0), (2, 1), (-2, 2)\)[/tex]
These match our expected pairs perfectly.
Choice D:
[tex]\((-2, -14), (-1, -10), (0, -6), (1, -2), (2, 2)\)[/tex]
These do not match our expected pairs.
Hence, the choice that contains the ordered pairs found on the graph of the inverse function is:
C. [tex]\((14, -2), (10, -1), (6, 0), (2, 1), (-2, 2)\)[/tex]
