To determine which set of ordered pairs represents a function, recall that a function is defined as a relation where each input (or $x$-value) corresponds to exactly one output (or $y$-value). This means no $x$-value can repeat with a different $y$-value.

Let's analyze each option:

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

   • The $x$-value $-2$ appears twice, with different $y$-values ($1$ and $5$). This violates the definition of a function.
   • Not a function.

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

   • The $x$-value $-6$ appears twice, with different $y$-values ($-4$ and $4$).
   • The $x$-value $-4$ also repeats with $-2$ and $2$.
   • Not a function.

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

   • All $x$-values ($-5, -3, -1, 1, 3$) are unique, and each corresponds to a single $y$-value.
   • This is a function.

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

   • The $x$-value $-1$ repeats multiple times, with different $y$-values ($5, 4, 3, 2, 1$).
   • Not a function.

Correct Answer:

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

Do you want a more detailed explanation or have additional questions?
Here are some related questions to explore:

1. What is the definition of a function in mathematical terms?
2. How can we determine whether a graph represents a function?
3. Can an $x$-value repeat in a function if it has the same $y$-value?
4. What is the difference between a relation and a function?
5. How does the vertical line test relate to functions?

Tip: Always check if any $x$-value appears more than once with different $y$-values when identifying functions.