Let's first review the tables given and check which ones represent inverse relations.

Table 1

x	-2	-1	0	1	2
y	2	1	0	-2	-1

Table 2

x	-2	-1	0	1	2
y	0	2	1	-2	-1

Table 3

x	-2	-1	0	1	2
y	1	2	-2	0	-1

Step 1: Identify inverse relations

Two tables represent inverse relations if, for every pair $(x_1, y_1)$ in one table, the pair $(y_1, x_1)$ appears in the other table.

• Table 1 and Table 2:

  • Let's compare the pairs from Table 1 with Table 2.
  • Table 1: $(-2, 2), (-1, 1), (0, 0), (1, -2), (2, -1)$
  • Table 2: $(-2, 0), (-1, 2), (0, 1), (1, -2), (2, -1)$

  We observe that the pairs match up exactly when the x and y values are swapped. Therefore, Table 1 and Table 2 are inverses.

• Table 1 and Table 3:

  • Table 1: $(-2, 2), (-1, 1), (0, 0), (1, -2), (2, -1)$
  • Table 3: $(-2, 1), (-1, 2), (0, -2), (1, 0), (2, -1)$

  The pairs do not match up as inverses because swapping the x and y does not lead to a consistent match between these tables. Therefore, Table 1 and Table 3 are not inverses.

• Table 2 and Table 3:

  • Table 2: $(-2, 0), (-1, 2), (0, 1), (1, -2), (2, -1)$
  • Table 3: $(-2, 1), (-1, 2), (0, -2), (1, 0), (2, -1)$

  These tables do not show inverse relationships either. Swapping the x and y values does not consistently result in corresponding pairs. Therefore, Table 2 and Table 3 are not inverses.

Step 2: Create the inverse for Table 3

We are now tasked with creating the inverse for Table 3. To do so, we need to swap the x and y values from the original table.

Table 3:

x	-2	-1	0	1	2
y	1	2	-2	0	-1

Now swap the x and y values:

• For $(-2, 1)$, the inverse pair will be $(1, -2)$
• For $(-1, 2)$, the inverse pair will be $(2, -1)$
• For $(0, -2)$, the inverse pair will be $(-2, 0)$
• For $(1, 0)$, the inverse pair will be $(0, 1)$
• For $(2, -1)$, the inverse pair will be $(-1, 2)$

Thus, the inverse table (Table 4) will be:

x	-2	-1	0	1	2
y	-2	-1	0	1	2

Final Answer:

• Table 1 and Table 2 represent inverse relations.
• The inverse of Table 3 is Table 4 with the y-values: -2, -1, 0, 1, 2.

Do you need any further clarification or explanation? Would you like to explore more about inverse relations or other concepts? Here's a list of related questions:

1. How do you verify if two relations are inverses algebraically?
2. What are the properties of inverse functions in relation to tables?
3. Can you identify other examples of inverse relations in other contexts?
4. How can we graphically represent inverse relations?
5. What happens when two relations are not inverses? How can they still be related?

Tip: To check if two relations are inverses, simply swap the x and y coordinates from one table and compare them to the second table. If they match, they are inverses!