To determine which sets of ordered pairs represent functions from $A$ to $B$, we must recall that a function from set $A$ to set $B$ assigns each element in $A$ to exactly one element in $B$. In other words, no element in $A$ can have more than one output in $B$.

Given $A = \{3, 4, 5, 6\}$ and $B = \{-2, -1, 0, 1, 2\}$, let's analyze each set of ordered pairs:

1. Set 1: $\{(3, 0), (4, 0), (5, 0), (6, 0)\}$

   • Each element of $A$ is mapped to exactly one element of $B$.
   • All elements from $A$ are paired with exactly one element from $B$ (in this case, all are paired with $0$).
   • This is a valid function.

2. Set 2: $\{(3, 1), (4, -2), (5, 0), (6, 2)\}$

   • Each element of $A$ is mapped to exactly one element of $B$, with no repeated inputs.
   • This is a valid function.

3. Set 3: $\{(3, -1), (5, 2), (4, -2), (6, 0), (4, 1)\}$

   • The element $4$ from $A$ is mapped to both $-2$ and $1$, which violates the definition of a function (one input cannot have multiple outputs).
   • This is not a function.

4. Set 4: $\{(3, 2), (6, 0), (4, 1)\}$

   • Each element of $A$ is mapped to exactly one element of $B$, with no repeated inputs.
   • This is a valid function.

Conclusion:

• Valid functions: Sets 1, 2, and 4.
• Not a function: Set 3.

Would you like more details on why certain sets are not functions or have any other questions?

Here are 5 related questions to extend your understanding:

1. What are the key characteristics of a function between two sets?
2. Can a function map multiple elements from $A$ to the same element in $B$?
3. What is the difference between a function and a relation?
4. How would you determine if a graph represents a function?
5. Can a function have more than one output for a single input?

Tip: When determining if a set of ordered pairs represents a function, check if any input is associated with more than one output—this violates the definition of a function.