To determine which set of ordered pairs represents $y$ as a function of $x$, we need to check if each $x$-value is paired with only one $y$-value. A function ensures that no $x$-value is repeated with different $y$-values.

• Option A: $\{(8, 4), (8, 6), (8, 1), (8, 0)\}$: The $x$-value $8$ is repeated with multiple $y$-values, so this is not a function.
• Option B: $\{(5, 4), (-9, 6), (-4, 0), (-3, -5)\}$: Each $x$-value is paired with a unique $y$-value. This is a function.
• Option C: $\{(-2, 7), (-3, 3), (-2, 8), (-3, -1)\}$: The $x$-values $-2$ and $-3$ are repeated with different $y$-values, so this is not a function.
• Option D: $\{(-3, 4), (-7, 0), (3, 0), (-7, -1)\}$: The $x$-value $-7$ is repeated with multiple $y$-values, so this is not a function.

Correct Answer: B

Would you like me to delve deeper into why functions are defined this way or explore related examples?

Questions:

1. What is the definition of a function in terms of $x$ and $y$?
2. Why is it problematic for an $x$-value to have multiple $y$-values?
3. Can a single $y$-value correspond to multiple $x$-values in a function?
4. What are some real-life examples where functions are used?
5. How does the vertical line test relate to this problem?

Tip: To verify a function quickly, check for repeated $x$-values with different $y$-values!