Which set of ordered pairs does *not* represent a function?

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Multiple Choice Answers

left curly bracket, left parenthesis, minus, 3, comma, 9, right parenthesis, comma, left parenthesis, 1, comma, 5, right parenthesis, comma, left parenthesis, 9, comma, minus, 8, right parenthesis, comma, left parenthesis, 6, comma, 1, right parenthesis, right curly bracket{(−3,9),(1,5),(9,−8),(6,1)}

left curly bracket, left parenthesis, 9, comma, minus, 2, right parenthesis, comma, left parenthesis, minus, 3, comma, 7, right parenthesis, comma, left parenthesis, 0, comma, minus, 4, right parenthesis, comma, left parenthesis, minus, 3, comma, 3, right parenthesis, right curly bracket{(9,−2),(−3,7),(0,−4),(−3,3)}

left curly bracket, left parenthesis, 4, comma, minus, 1, right parenthesis, comma, left parenthesis, minus, 3, comma, 1, right parenthesis, comma, left parenthesis, 6, comma, minus, 7, right parenthesis, comma, left parenthesis, 7, comma, minus, 1, right parenthesis, right curly bracket{(4,−1),(−3,1),(6,−7),(7,−1)}

left curly bracket, left parenthesis, 6, comma, minus, 4, right parenthesis, comma, left parenthesis, 3, comma, 3, right parenthesis, comma, left parenthesis, minus, 3, comma, minus, 7, right parenthesis, comma, left parenthesis, minus, 2, comma, minus, 4, right parenthesis, right curly bracket{(6,−4),(3,3),(−3,−7),(−2,−4)}

To determine which set of ordered pairs does not represent a function, we need to check if any input (the first element in each pair) is repeated with a different output (the second element in the pair). 

A set of ordered pairs represents a function if and only if each input corresponds to exactly one output.

Let's examine each option:

1. **{(-3,9), (1,5), (9,-8), (6,1)}**
   - Inputs: -3, 1, 9, 6
   - No input is repeated.

2. **{(9,-2), (-3,7), (0,-4), (-3,3)}**
   - Inputs: 9, -3, 0, -3
   - The input -3 is repeated with different outputs (7 and 3). **This is not a function.**

3. **{(4,-1), (-3,1), (6,-7), (7,-1)}**
   - Inputs: 4, -3, 6, 7
   - No input is repeated.

4. **{(6,-4), (3,3), (-3,-7), (-2,-4)}**
   - Inputs: 6, 3, -3, -2
   - No input is repeated.

The correct answer is the second set: **{(9,-2), (-3,7), (0,-4), (-3,3)}**. This set does not represent a function because the input `-3` is associated with two different outputs (`7` and `3`).

Would you like more details or have any questions? Here are five related questions you might find interesting:

1. What defines a function in mathematics?
2. Can a function have the same output for different inputs?
3. What is the vertical line test for functions?
4. How do you represent a function using a graph?
5. What are some common examples of functions in real life?

**Tip:** When determining if a set of ordered pairs represents a function, focus on ensuring that each input value maps to only one output value.

Understand how to identify functions in ordered pairs with clear examples. Learn why certain sets of ordered pairs do not represent functions, including detailed explanations and solutions. Suitable for Grades 9-12.

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