Question

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

which tables represent relations that are inverses

Answer 1

To determine if two relations are inverses of each other, we need to confirm whether each pair of points \((x_1, y_1)\) from one table corresponds to the pair \((y_1, x_1)\) from the other table. This means if \((x, y)\) exists in one table, then \((y, x)\) should exist in the second table.

Let's analyze the given tables:

1. **Table 1:**
- Points: \((-2, 2), (-1, 1), (0, 0), (1, -2), (2, -1)\)

2. **Table 2:**
- Points: \((-2, 0), (-1, 2), (0, 1), (1, -2), (2, -1)\)

3. **Table 3:**
- Points: \((-2, 1), (-1, 2), (0, -2), (1, 0), (2, -1)\)

Now, let's check pairs between each table:
- **Table 1 and Table 2:**
- Table 1 has point \((-2, 2)\). Table 2 does not have point \((2, -2)\).
- Conclusion: Not inverses.

- **Table 1 and Table 3:**
- Table 1 has point \((-2, 2)\). Table 3 does not have point \((2, -2)\).
- Conclusion: Not inverses.

- **Table 2 and Table 3:**
- Table 2 has point \((-2, 0)\). Table 3 does not have point \((0, -2)\).
- Conclusion: Not inverses.

Since no pair of tables satisfies the conditions for being inverses of each other, **none of the tables represent relations that are inverses.**