Match each table with its equation.

1. [tex]$ \square $[/tex] [tex]$ y = x $[/tex]
2. [tex]$ \square $[/tex] [tex]$ y = \sqrt{x} $[/tex]
3. [tex]$ \square $[/tex] [tex]$ y = \frac{1}{x} $[/tex]
4. [tex]$ \square $[/tex] [tex]$ y = x^2 $[/tex]
5. [tex]$ \square $[/tex] [tex]$ y = x^3 $[/tex]
6. [tex]$ \square $[/tex] [tex]$ y = |x| $[/tex]

a.
\begin{tabular}{|r|r|}
\hline Input & Output \\
\hline -2 & 2 \\
\hline -1 & 1 \\
\hline 0 & 0 \\
\hline 1 & 1 \\
\hline 2 & 2 \\
\hline 3 & 3 \\
\hline
\end{tabular}

b.
\begin{tabular}{|r|r|}
\hline Input & Output \\
\hline -2 & - \\
\hline -1 & - \\
\hline 0 & 0 \\
\hline 1 & 1 \\
\hline 4 & 2 \\
\hline 9 & 3 \\
\hline
\end{tabular}

c.
\begin{tabular}{|r|r|}
\hline Input & Output \\
\hline -2 & -8 \\
\hline -1 & -1 \\
\hline 0 & 0 \\
\hline 1 & 1 \\
\hline 2 & 8 \\
\hline 3 & 27 \\
\hline
\end{tabular}

d.
\begin{tabular}{|r|r|}
\hline Input & Output \\
\hline -2 & -0.5 \\
\hline -1 & -1 \\
\hline 0 & - \\
\hline 1 & 1 \\
\hline 2 & 0.5 \\
\hline 3 & 0.33 \\
\hline
\end{tabular}

e.
\begin{tabular}{|r|r|}
\hline Input & Output \\
\hline -2 & -2 \\
\hline -1 & -1 \\
\hline 0 & 0 \\
\hline 1 & 1 \\
\hline 2 & 2 \\
\hline 3 & 3 \\
\hline
\end{tabular}

f.
\begin{tabular}{|r|r|}
\hline Input & Output \\
\hline -2 & 4 \\
\hline -1 & 1 \\
\hline 0 & 0 \\
\hline 1 & 1 \\
\hline 2 & 4 \\
\hline
\end{tabular}

To solve this problem, we need to match each table to its corresponding equation.

We are given the following equations:
1. [tex]$ y = x $[/tex]
2. [tex]$ y = \sqrt{x} $[/tex]
3. [tex]$ y = \frac{1}{x} $[/tex]
4. [tex]$ y = x^2 $[/tex]
5. [tex]$ y = x^3 $[/tex]
6. [tex]$ y = |x| $[/tex]

Let's analyze each table:

Table a:
[tex]\[ \begin{tabular}{|r|r|} \hline Input & Output \\ \hline -2 & 2 \\ \hline -1 & 1 \\ \hline 0 & 0 \\ \hline 1 & 1 \\ \hline 2 & 2 \\ \hline 3 & 3 \\ \hline \end{tabular} \][/tex]
For table a:
- When [tex]$ x = -2 $[/tex], [tex]$ y = 2 $[/tex]
- When [tex]$ x = -1 $[/tex], [tex]$ y = 1 $[/tex]
- When [tex]$ x = 0 $[/tex], [tex]$ y = 0 $[/tex]
- When [tex]$ x = 1 $[/tex], [tex]$ y = 1 $[/tex]
- When [tex]$ x = 2 $[/tex], [tex]$ y = 2 $[/tex]
- When [tex]$ x = 3 $[/tex], [tex]$ y = 3 $[/tex]

This table corresponds to the equation [tex]$ y = |x| $[/tex].

Table b:
[tex]\[ \begin{tabular}{|r|r|} \hline Input & Output \\ \hline -2 & - \\ \hline -1 & - \\ \hline 0 & 0 \\ \hline 1 & 1 \\ \hline 4 & 2 \\ \hline 9 & 3 \\ \hline \end{tabular} \][/tex]
For table b, only non-negative inputs have defined outputs:
- When [tex]$ x = 0 $[/tex], [tex]$ y = 0 $[/tex]
- When [tex]$ x = 1 $[/tex], [tex]$ y = 1 $[/tex]
- When [tex]$ x = 4 $[/tex], [tex]$ y = 2 $[/tex]
- When [tex]$ x = 9 $[/tex], [tex]$ y = 3 $[/tex]

This table corresponds to the equation [tex]$ y = \sqrt{x} $[/tex].

Table c:
[tex]\[ \begin{tabular}{|r|r|} \hline Input & Output \\ \hline -2 & -8 \\ \hline -1 & -1 \\ \hline 0 & 0 \\ \hline 1 & 1 \\ \hline 2 & 8 \\ \hline 3 & 27 \\ \hline \end{tabular} \][/tex]
For table c:
- When [tex]$ x = -2 $[/tex], [tex]$ y = -8 $[/tex]
- When [tex]$ x = -1 $[/tex], [tex]$ y = -1 $[/tex]
- When [tex]$ x = 0 $[/tex], [tex]$ y = 0 $[/tex]
- When [tex]$ x = 1 $[/tex], [tex]$ y = 1 $[/tex]
- When [tex]$ x = 2 $[/tex], [tex]$ y = 8 $[/tex]
- When [tex]$ x = 3 $[/tex], [tex]$ y = 27 $[/tex]

This table corresponds to the equation [tex]$ y = x^3 $[/tex].

Table d:
[tex]\[ \begin{tabular}{|r|r|} \hline Input & Output \\ \hline -2 & -0.5 \\ \hline -1 & -1 \\ \hline 0 & - \\ \hline 1 & 1 \\ \hline 2 & 0.5 \\ \hline 3 & 0.33 \\ \hline \end{tabular} \][/tex]
For table d:
- When [tex]$ x = -2 $[/tex], [tex]$ y = -0.5 $[/tex]
- When [tex]$ x = -1 $[/tex], [tex]$ y = -1 $[/tex]
- When [tex]$ x = 0 $[/tex], [tex]$ y $[/tex] is undefined
- When [tex]$ x = 1 $[/tex], [tex]$ y = 1 $[/tex]
- When [tex]$ x = 2 $[/tex], [tex]$ y = 0.5 $[/tex]
- When [tex]$ x = 3 $[/tex], [tex]$ y = 0.33 $[/tex]

This table corresponds to the equation [tex]$ y = \frac{1}{x} $[/tex].

Table e:
[tex]\[ \begin{tabular}{|r|r|} \hline Input & Output \\ \hline -2 & -2 \\ \hline -1 & -1 \\ \hline 0 & 0 \\ \hline 1 & 1 \\ \hline 2 & 2 \\ \hline 3 & 3 \\ \hline \end{tabular} \][/tex]
For table e:
- When [tex]$ x = -2 $[/tex], [tex]$ y = -2 $[/tex]
- When [tex]$ x = -1 $[/tex], [tex]$ y = -1 $[/tex]
- When [tex]$ x = 0 $[/tex], [tex]$ y = 0 $[/tex]
- When [tex]$ x = 1 $[/tex], [tex]$ y = 1 $[/tex]
- When [tex]$ x = 2 $[/tex], [tex]$ y = 2 $[/tex]
- When [tex]$ x = 3 $[/tex], [tex]$ y = 3 $[/tex]

This table corresponds to the equation [tex]$ y = x $[/tex].

Table f:
[tex]\[ \begin{tabular}{|r|r|} \hline Input & Output \\ \hline -2 & 4 \\ \hline -1 & 1 \\ \hline 0 & 0 \\ \hline 1 & 1 \\ \hline 2 & 4 \\ \hline \end{tabular} \][/tex]
For table f:
- When [tex]$ x = -2 $[/tex], [tex]$ y = 4 $[/tex]
- When [tex]$ x = -1 $[/tex], [tex]$ y = 1 $[/tex]
- When [tex]$ x = 0 $[/tex], [tex]$ y = 0 $[/tex]
- When [tex]$ x = 1 $[/tex], [tex]$ y = 1 $[/tex]
- When [tex]$ x = 2 $[/tex], [tex]$ y = 4 $[/tex]

This table corresponds to the equation [tex]$ y = x^2 $[/tex].

Hence, the matching is:
- [tex]$ y = x $[/tex]: Table e
- [tex]$ y = \sqrt{x} $[/tex]: Table b
- [tex]$ y = \frac{1}{x} $[/tex]: Table d
- [tex]$ y = x^2 $[/tex]: Table f
- [tex]$ y = x^3 $[/tex]: Table c
- [tex]$ y = |x| $[/tex]: Table a