Question

Consider the following tables, each representing a relation. 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 Question 1 A. Identify the two tables that represent relations that are inverses.(2 points) Table # and Table #

Answer 1

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Answer 2

To identify which tables represent relations that are inverses, we need to check the pairs of (x, y) values in each table and see if swapping the x and y values yields another table.

Let's analyze each table:

**Table #1:**
- (-2, 2)
- (-1, 1)
- (0, 0)
- (1, -2)
- (2, -1)

**Table #2:**
- (-2, 0)
- (-1, 2)
- (0, 1)
- (1, -2)
- (2, -1)

**Table #3:**
- (-2, 1)
- (-1, 2)
- (0, -2)
- (1, 0)
- (2, -1)

Now let's look for inverse relationships:

1. Checking Table #1 and Table #2:
- For Table #1, (-2, 2) should correspond to (2, -2) in Table #2.
- The pairs do not match, so Table #1 and Table #2 are not inverses.

2. Checking Table #1 and Table #3:
- For Table #1, (-2, 2) should correspond to (2, -2) in Table #3.
- The pairs do not match, so Table #1 and Table #3 are not inverses.

3. Checking Table #2 and Table #3:
- For Table #2, (-2, 0) does not correspond to (0, -2) in Table #3, so they are not inverses.
- For Table #2, (-1, 2) corresponds to (2, -1) in Table #3 and matches as an inverse.
- For Table #2, (0, 1) corresponds to (1, 0) in Table #3 which also matches.
- For Table #2, (1, -2) corresponds to (-2, 1) in Table #3 which also matches.
- Finally, for Table #2, (2, -1) corresponds to (-1, 2) in Table #3 which also matches.

Since all pairs of values in Table #2 and Table #3 are inverses of each other, we conclude that:

**Table #2 and Table #3 represent relations that are inverses.**

**Answer:** Table #2 and Table #3.