Answer :
To determine which set of ordered pairs represents a function, we need to check if each input [tex]\( x \)[/tex] in the set is associated with exactly one output [tex]\( y \)[/tex]. In other words, for the relation to be a function, each [tex]\( x \)[/tex] value must appear only once in the set of ordered pairs.
Let's analyze each set of pairs:
### Set A: [tex]\(\{(-8,-14),(-7,-12),(-6,-10),(-5,-8)\}\)[/tex]
- Examine the [tex]\( x \)[/tex]-values: [tex]\(-8, -7, -6, -5\)[/tex]
- Each [tex]\( x \)[/tex] value is unique.
- Therefore, Set A represents a function.
### Set B: [tex]\(\{(-4,-14),(-9,-12),(-6,-10),(-9,-8)\}\)[/tex]
- Examine the [tex]\( x \)[/tex]-values: [tex]\(-4, -9, -6, -9\)[/tex]
- Notice that the [tex]\( x \)[/tex] value [tex]\(-9\)[/tex] appears twice, with different [tex]\( y \)[/tex]-values [tex]\(-12\)[/tex] and [tex]\(-8\)[/tex].
- Therefore, Set B does not represent a function.
### Set C: [tex]\(\{(8,-2),(9,-1),(10,2),(8,-10)\}\)[/tex]
- Examine the [tex]\( x \)[/tex]-values: [tex]\(8, 9, 10, 8\)[/tex]
- Notice that the [tex]\( x \)[/tex] value [tex]\(8\)[/tex] appears twice, with different [tex]\( y \)[/tex]-values [tex]\(-2\)[/tex] and [tex]\(-10\)[/tex].
- Therefore, Set C does not represent a function.
### Set D: [tex]\(\{(-8,-6),(-5,-3),(-2,0),(-2,3)\}\)[/tex]
- Examine the [tex]\( x \)[/tex]-values: [tex]\(-8, -5, -2, -2\)[/tex]
- Notice that the [tex]\( x \)[/tex] value [tex]\(-2\)[/tex] appears twice, with different [tex]\( y \)[/tex]-values [tex]\(0\)[/tex] and [tex]\(3\)[/tex].
- Therefore, Set D does not represent a function.
In summary, only Set A meets the criteria for being a function.
Thus, the correct answer is:
A. [tex]\(\{(-8,-14),(-7,-12),(-6,-10),(-5,-8)\}\)[/tex]
Let's analyze each set of pairs:
### Set A: [tex]\(\{(-8,-14),(-7,-12),(-6,-10),(-5,-8)\}\)[/tex]
- Examine the [tex]\( x \)[/tex]-values: [tex]\(-8, -7, -6, -5\)[/tex]
- Each [tex]\( x \)[/tex] value is unique.
- Therefore, Set A represents a function.
### Set B: [tex]\(\{(-4,-14),(-9,-12),(-6,-10),(-9,-8)\}\)[/tex]
- Examine the [tex]\( x \)[/tex]-values: [tex]\(-4, -9, -6, -9\)[/tex]
- Notice that the [tex]\( x \)[/tex] value [tex]\(-9\)[/tex] appears twice, with different [tex]\( y \)[/tex]-values [tex]\(-12\)[/tex] and [tex]\(-8\)[/tex].
- Therefore, Set B does not represent a function.
### Set C: [tex]\(\{(8,-2),(9,-1),(10,2),(8,-10)\}\)[/tex]
- Examine the [tex]\( x \)[/tex]-values: [tex]\(8, 9, 10, 8\)[/tex]
- Notice that the [tex]\( x \)[/tex] value [tex]\(8\)[/tex] appears twice, with different [tex]\( y \)[/tex]-values [tex]\(-2\)[/tex] and [tex]\(-10\)[/tex].
- Therefore, Set C does not represent a function.
### Set D: [tex]\(\{(-8,-6),(-5,-3),(-2,0),(-2,3)\}\)[/tex]
- Examine the [tex]\( x \)[/tex]-values: [tex]\(-8, -5, -2, -2\)[/tex]
- Notice that the [tex]\( x \)[/tex] value [tex]\(-2\)[/tex] appears twice, with different [tex]\( y \)[/tex]-values [tex]\(0\)[/tex] and [tex]\(3\)[/tex].
- Therefore, Set D does not represent a function.
In summary, only Set A meets the criteria for being a function.
Thus, the correct answer is:
A. [tex]\(\{(-8,-14),(-7,-12),(-6,-10),(-5,-8)\}\)[/tex]
