To determine which of the given sets of ordered pairs represents a function, we need to recall the definition of a function. A relation is a function if and only if each input (domain value) corresponds to exactly one output (range value). In other words, no x-value (input) is repeated with a different y-value (output).
Let's analyze each set of ordered pairs:
1. [tex]\(\{(-6, -5), (-4, -3), (-2, 0), (-2, 2), (0, 4)\}\)[/tex]
- Here, -2 is associated with two different range values (0 and 2). Thus, this set cannot represent a function, as it violates the definition.
2. [tex]\(\{(-5, -5), (-5, -4), (-5, -3), (-5, -2), (-5, 0)\}\)[/tex]
- In this set, -5 is associated with multiple different range values (-5, -4, -3, -2, and 0). Again, this set cannot represent a function because a single value from the domain maps to multiple values in the range.
3. [tex]\(\{(-4, -5), (-3, 0), (-2, -4), (0, -3), (2, -2)\}\)[/tex]
- Each domain value (-4, -3, -2, 0, 2) is paired with exactly one unique range value. No x-value is repeated with a different y-value. Thus, this set represents a function.
4. [tex]\(\{(-6, -3), (-6, -2), (-5, -3), (-3, -3), (0, 0)\}\)[/tex]
- Here, -6 is associated with two different range values (-3 and -2). Therefore, this set cannot represent a function as it violates the function definition.
From this analysis, the set of ordered pairs that represents a function is:
[tex]\(\{(-4, -5), (-3, 0), (-2, -4), (0, -3), (2, -2)\}\)[/tex]
Therefore, the correct answer is the third set of ordered pairs.
The correct answer is:
[tex]\(\{(-4, -5), (-3, 0), (-2, -4), (0, -3), (2, -2)\}\)[/tex]
