To determine which of the given answer choices represent a relation that is a function, let's review the definition of a function. A relation is a function if and only if for each input (x-coordinate), there is exactly one output (y-coordinate). In other words, no x-coordinate is repeated with a different y-coordinate.
We will analyze each set of ordered pairs provided in the answer choices:
1. [tex]\(\{(-1,6),(4,4),(7,13),(4,8)\}\)[/tex]
- Here, the x-coordinate 4 is associated with both 4 and 8.
- Since the x-coordinate 4 is repeated with different y-coordinates, this relation is not a function.
2. [tex]\(\{(3,6),(3,5),(9,12),(0,-3)\}\)[/tex]
- The x-coordinate 3 is associated with both 6 and 5.
- Since the x-coordinate 3 is repeated with different y-coordinates, this relation is not a function.
3. [tex]\(\{(-5,0),(6,8),(3,-5),(-5,-3)\}\)[/tex]
- The x-coordinate -5 is associated with both 0 and -3.
- Since the x-coordinate -5 is repeated with different y-coordinates, this relation is not a function.
4. [tex]\(\{(7,9),(8,4),(-2,4),(-3,14)\}\)[/tex]
- Here, each x-coordinate (7, 8, -2, and -3) is unique.
- Since no x-coordinate is repeated, this relation is a function.
5. [tex]\(\{(8,3),(3,7),(6,4),(5,4)\}\)[/tex]
- Here, each x-coordinate (8, 3, 6, and 5) is unique.
- Since no x-coordinate is repeated, this relation is a function.
Based on the analysis, the relations that are functions are:
[tex]\[
\boxed{4}, \boxed{5}
\][/tex]
