To determine which table represents a function, we need to remember that a function assigns exactly one output (y-value) for each input (x-value). In other words, no x-value should have more than one corresponding y-value.

Let's analyze each table:

1. First Table:

   • $(-5, -5)$, $(0, 0)$, $(5, 5)$, $(6, -6)$
   • Each x-value has a unique y-value.
   • This is a function.

2. Second Table:

   • $(-4, 8)$, $(-2, 8)$, $(0, 2)$
   • Each x-value has a unique y-value.
   • This is a function.

3. Third Table:

   • $(-3, -1)$, $(-2, 0)$, $(-2, -1)$, $(8, 1)$
   • The x-value $-2$ corresponds to both $0$ and $-1$.
   • This is not a function.

4. Fourth Table:

   • $(-4, 2)$, $(-3, 1)$, $(1, 3)$, $(4, 0)$
   • Each x-value has a unique y-value.
   • This is a function.

Based on this analysis, the tables that represent functions are the first, second, and fourth tables. The third table does not represent a function because the x-value $-2$ corresponds to two different y-values.

Would you like to ask anything specific or go into more details?

Here are 5 questions to expand your understanding:

1. What is the definition of a function in mathematical terms?
2. How can you determine if a graph represents a function?
3. Can a function have the same y-value for different x-values?
4. What is the difference between a function and a relation?
5. What are some examples of real-life situations where functions are used?

Tip: Remember, a quick way to check if a table represents a function is to ensure that no x-value is repeated with different y-values.