To determine which of the given sets of ordered pairs is a function, we need to check if each input (first element of the pair) corresponds to exactly one output (second element of the pair).

Definition of a Function

A function assigns each input value (domain) to one and only one output value (range). If an input appears multiple times with different outputs, then it is not a function.

Checking Each Option:

Option A: { (0, 0), (0, 2), (2, 0), (2, 2) }

• The input 0 is associated with both 0 and 2.
• The input 2 is associated with both 0 and 2.
  ❌ Not a function because inputs have multiple outputs.

Option B: { (2, 2), (2, 3), (3, 2), (3, 3) }

• The input 2 is associated with both 2 and 3.
• The input 3 is associated with both 2 and 3.
  ❌ Not a function because inputs have multiple outputs.

Option C: { (2, -1), (2, 1), (3, -1), (3, 1) }

• The input 2 is associated with both -1 and 1.
• The input 3 is associated with both -1 and 1.
  ❌ Not a function because inputs have multiple outputs.

Option D: { (-2, -3), (-3, -2), (2, 3), (3, 2) }

• Each input value appears only once.
• Input -2 → -3, input -3 → -2, input 2 → 3, input 3 → 2.
  ✅ This is a function because each input has exactly one output.

Final Answer:

Option D is the correct answer because it satisfies the definition of a function.

Would you like further details or explanations? Here are some related questions to expand your understanding:

1. What is the difference between a relation and a function?
2. How can you represent a function using a graph?
3. What is the vertical line test for determining functions?
4. How do you identify the domain and range of a function?
5. Can a function have the same output for different inputs?

Tip: To check if a relation is a function, ensure no input value maps to more than one output.