To determine which set of ordered pairs is not a function, we need to understand the definition of a function. In a function, each input [tex]\( x \)[/tex] must map to exactly one output [tex]\( y \)[/tex]. This means that no [tex]\( x \)[/tex] value can be associated with more than one [tex]\( y \)[/tex] value.
Let's analyze each given set of ordered pairs:
1. [tex]\(\{(-2, -2), (-1, -1), (1, 1), (2, 2)\}\)[/tex]
In this set, the [tex]\( x \)[/tex] values are [tex]\(-2, -1, 1, 2\)[/tex]. Each of these [tex]\( x \)[/tex] values is unique and maps to exactly one [tex]\( y \)[/tex] value.
- (-2) maps to (-2)
- (-1) maps to (-1)
- (1) maps to (1)
- (2) maps to (2)
This set is a function.
2. [tex]\(\{(-1, 2), (0, 0), (-1, -2), (-2, -3)\}\)[/tex]
In this set, the [tex]\( x \)[/tex] values are [tex]\(-1, 0, -1, -2\)[/tex]. Notice that the [tex]\( x \)[/tex] value [tex]\( -1 \)[/tex] is repeated; it maps to both 2 and -2.
- (-1) maps to 2
- (0) maps to (0)
- (-1) maps to (-2)
- (-2) maps to (-3)
Since the [tex]\( x \)[/tex] value of [tex]\(-1\)[/tex] is associated with more than one [tex]\( y \)[/tex] value, this set is not a function.
3. [tex]\(\{(4, 2), (3, 1), (2, 0), (1, -1)\}\)[/tex]
In this set, the [tex]\( x \)[/tex] values are [tex]\( 4, 3, 2, 1 \)[/tex]. Each of these [tex]\( x \)[/tex] values is unique and maps to exactly one [tex]\( y \)[/tex] value.
- (4) maps to 2
- (3) maps to 1
- (2) maps to 0
- (1) maps to -1
This set is a function.
4. [tex]\(\{(2, 1), (4, 1), (6, 1), (8, 1)\}\)[/tex]
In this set, the [tex]\( x \)[/tex] values are [tex]\( 2, 4, 6, 8 \)[/tex]. Each of these [tex]\( x \)[/tex] values is unique and maps to exactly one [tex]\( y \)[/tex] value.
- (2) maps to (1)
- (4) maps to (1)
- (6) maps to (1)
- (8) maps to (1)
This set is a function, even though multiple [tex]\( x \)[/tex] values map to the same [tex]\( y \)[/tex] value, each [tex]\( x \)[/tex] maps to a single [tex]\( y \)[/tex].
Therefore, the set of ordered pairs that is not a function is:
[tex]\[
\{(-1, 2), (0, 0), (-1, -2), (-2, -3)\}
\][/tex]
This corresponds to the second set. Therefore, the answer is:
[tex]\[
\boxed{2}
\][/tex]
