To determine if a set of points represents a function, we apply the definition of a function:

A function is a relation where every input (x-value) has exactly one unique output (y-value). In other words, no two pairs should have the same x-value associated with different y-values.

Let’s analyze the given set of points:
$\{(-4, 8), (2, 1), (7, 12), (3, 12)\}$

• The x-values are: -4, 2, 7, and 3.
• Each x-value is unique and corresponds to exactly one y-value:
  • -4 → 8
  • 2 → 1
  • 7 → 12
  • 3 → 12

Since no x-value is repeated, this set of points is a function.

The correct answer is Yes.

Would you like further details or have any questions?

Here are 5 related questions to expand on this:

1. What is the vertical line test and how does it relate to functions?
2. How would the answer change if one x-value had two different y-values?
3. Can a relation with repeating y-values still be a function? Why?
4. What are some examples of real-life situations that can be modeled as functions?
5. How would this analysis change if we considered a continuous graph instead of discrete points?

Tip: When determining if a relation is a function, focus only on the x-values (inputs) and ensure none of them are assigned to multiple y-values.