To analyze each relation, let’s go through the tables in the image and answer each question:

A. Which table(s) do not represent a function?

A relation is a function if every $x$-value has a unique $y$-value.

1. Relation 1: Each $x$-value has a unique $y$-value.
2. Relation 2: Each $x$-value has a unique $y$-value.
3. Relation 3: Each $x$-value has a unique $y$-value.
4. Relation 4: Each $x$-value has a unique $y$-value.

Answer: All tables represent functions.

B. Which table(s) represent a linear relationship?

To determine if a relation is linear, the change in $y$ values should be consistent as $x$ increases by a fixed amount.

1. Relation 1: The differences between consecutive $y$-values (3, 5, 7, 9, 11) are consistent, indicating a linear relationship.
2. Relation 2: The differences between $y$-values (31, 28, 25, 22, 19) are consistent as well, indicating a linear relationship.
3. Relation 3: The differences between $y$-values (3, 3, 3, 3) are consistent, indicating a linear relationship.
4. Relation 4: The differences between $y$-values (10, 20, 30, 40, 50) are also consistent, indicating a linear relationship.

Answer: All tables (Relations 1, 2, 3, and 4) represent linear relationships.

C. Which table(s) show a decreasing relationship?

A relationship is decreasing if $y$ values decrease as $x$ values increase.

1. Relation 1: $y$-values are increasing.
2. Relation 2: $y$-values are decreasing.
3. Relation 3: $y$-values are constant.
4. Relation 4: $y$-values are increasing.

Answer: Only Relation 2 shows a decreasing relationship.

If you need further details or have any questions, feel free to ask!

Here are some follow-up questions that expand on this topic:

1. What are the characteristics of a nonlinear relationship in a table format?
2. How can we determine if a function is increasing or decreasing just by looking at a graph?
3. Can a function have a mix of increasing and decreasing intervals? Give an example.
4. How would we identify if a table represents an exponential relationship?
5. What are the implications of having a constant function in real-world scenarios?

Tip: When analyzing tables for linear relationships, check if the difference between consecutive $y$-values is constant, as this indicates a linear pattern.