To determine which set of ordered pairs represents a function, we need to check if each input (or $x$-coordinate) corresponds to only one output (or $y$-coordinate). In other words, no $x$-value should be repeated with different $y$-values.

Let's analyze each option:

1. $\{(-4, -7), (8, 7), (8, 2), (-8, -4)\}$:

   • The $x$-value 8 appears twice with different $y$-values (7 and 2).
   • This set does not represent a function.

2. $\{(7, 6), (-1, 8), (-8, 0), (-1, -2)\}$:

   • The $x$-value $-1$ appears twice with different $y$-values (8 and -2).
   • This set does not represent a function.

3. $\{(2, 8), (-4, 1), (5, 0), (-8, 1)\}$:

   • All $x$-values are unique.
   • This set does represent a function.

4. $\{(2, 4), (2, -8), (-5, 0), (4, -6)\}$:

   • The $x$-value 2 appears twice with different $y$-values (4 and -8).
   • This set does not represent a function.

Correct Answer:

The set $\{(2, 8), (-4, 1), (5, 0), (-8, 1)\}$ (option 3) represents a function.

Would you like any more details or have any questions?

Related Questions:

1. What defines a relation as a function?
2. Can a function have the same $y$-value for different $x$-values?
3. How can the vertical line test be used to identify functions on a graph?
4. What is the difference between a one-to-one function and a many-to-one function?
5. How do you express a function algebraically instead of using ordered pairs?

Tip:

A quick way to verify if a set represents a function is to ensure that no $x$-value appears more than once with different $y$-values!