To determine which of the given sets of ordered pairs represents a function, we'll need to check if each [tex]\( x \)[/tex]-value in the set maps to exactly one [tex]\( y \)[/tex]-value. A set of ordered pairs is a function if no [tex]\( x \)[/tex]-value repeats with a different [tex]\( y \)[/tex]-value.
Let's analyze each set of ordered pairs one by one:
### Set 1: [tex]\(\{(-4, -3), (-2, -1), (-2, 0), (0, -2), (0, 2)\}\)[/tex]
- The [tex]\( x \)[/tex]-values are: [tex]\(-4, -2, -2, 0, 0\)[/tex].
- Notice that [tex]\(-2\)[/tex] corresponds to both [tex]\(-1\)[/tex] and [tex]\(0\)[/tex], and [tex]\(0\)[/tex] corresponds to both [tex]\(-2\)[/tex] and [tex]\(2\)[/tex].
Since there are repeated [tex]\( x \)[/tex]-values ([tex]\(-2\)[/tex] and [tex]\(0\)[/tex]) with different [tex]\( y \)[/tex]-values, this set does not represent a function.
### Set 2: [tex]\(\{(-5, -5), (-5, -4), (-5, -3), (-5, -2), (-3, 0)\}\)[/tex]
- The [tex]\( x \)[/tex]-values are: [tex]\(-5, -5, -5, -5, -3\)[/tex].
- Notice that [tex]\(-5\)[/tex] corresponds to [tex]\(-5\)[/tex], [tex]\(-4\)[/tex], [tex]\(-3\)[/tex], and [tex]\(-2\)[/tex], all different [tex]\( y \)[/tex]-values.
Since there are repeated [tex]\( x \)[/tex]-values ([tex]\(-5\)[/tex]) with different [tex]\( y \)[/tex]-values, this set does not represent a function.
### Set 3: [tex]\(\{(-4, -5), (-4, 0), (-3, -4), (0, -3), (3, -2)\}\)[/tex]
- The [tex]\( x \)[/tex]-values are: [tex]\(-4, -4, -3, 0, 3\)[/tex].
- Notice that [tex]\(-4\)[/tex] corresponds to both [tex]\(-5\)[/tex] and [tex]\(0\)[/tex].
Since there are repeated [tex]\( x \)[/tex]-values ([tex]\(-4\)[/tex]) with different [tex]\( y \)[/tex]-values, this set does not represent a function.
### Set 4: [tex]\(\{(-6, -3), (-4, -3), (-3, -3), (-2, -3), (0, 0)\}\)[/tex]
- The [tex]\( x \)[/tex]-values are: [tex]\(-6, -4, -3, -2, 0\)[/tex].
- In this set, each [tex]\( x \)[/tex]-value maps to exactly one [tex]\( y \)[/tex]-value ([tex]\(-3\)[/tex] for the first four and [tex]\(0\)[/tex] for the last one).
Since there are no repeated [tex]\( x \)[/tex]-values, this set does represent a function.
### Conclusion
Based on the analysis, the only set of ordered pairs that represents a function is:
[tex]\[
\{(-6, -3), (-4, -3), (-3, -3), (-2, -3), (0, 0)\}
\][/tex]
So the answer is:
[tex]\[
(False, False, False, True)
\][/tex]
