Which sets of ordered pairs represent functions from A to B? (Select all that apply.)
A = {3, 4, 5, 6} and B = {−2, −1, 0, 1, 2}

{(3, 0), (4, 0), (5, 0), (6, 0)}
 

{(3, 1), (4, −2), (5, 0), (6, 2)}
 

{(3, −1), (5, 2), (4, −2), (6, 0), (4, 1)}
 

{(3, 2), (6, 0), (4, 1)}
 


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.

Which sets of ordered pairs represent functions from A to B? (Select all that apply.) A = {3, 4, 5, 6} and B = {−2, −1, 0, 1, 2}

{(3, 0), (4, 0), (5, 0), (6, 0)}

{(3, 1), (4, −2), (5, 0), (6, 2)}

{(3, −1), (5, 2), (4, −2), (6, 0), (4, 1)}

{(3, 2), (6, 0), (4, 1)}

Learn how to identify valid functions from sets of ordered pairs with a detailed explanation. This problem explores key concepts of functions and relations, focusing on sets A = {3, 4, 5, 6} and B = {−2, −1, 0, 1, 2}. Suitable for students in Grades 8-10.

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