To determine which set of ordered pairs does not represent a function, we need to understand the definition of a function. A function from a set [tex]\( X \)[/tex] to a set [tex]\( Y \)[/tex] is a relation that assigns to each element of [tex]\( X \)[/tex] exactly one element of [tex]\( Y \)[/tex]. In other words, no two ordered pairs have the same first element (the input or [tex]\( x \)[/tex]-value).
Let's examine each set of ordered pairs given in the options to see if any of them do not satisfy this condition:
1. [tex]\(\{(-9, 5), (-2, -4), (-8, -6), (4, 5)\}\)[/tex]
Looking at the first elements:
[tex]\[ -9, -2, -8, 4 \][/tex]
All the [tex]\( x \)[/tex]-values are distinct. Therefore, this set represents a function.
2. [tex]\(\{(8, -1), (2, 9), (-3, -1), (-6, 4)\}\)[/tex]
Looking at the first elements:
[tex]\[ 8, 2, -3, -6 \][/tex]
All the [tex]\( x \)[/tex]-values are distinct. Therefore, this set represents a function.
3. [tex]\(\{(-2, 9), (9, 3), (-8, 9), (6, -1)\}\)[/tex]
Looking at the first elements:
[tex]\[ -2, 9, -8, 6 \][/tex]
All the [tex]\( x \)[/tex]-values are distinct. Therefore, this set represents a function.
4. [tex]\(\{(4, 1), (8, 2), (8, 7), (6, -2)\}\)[/tex]
Looking at the first elements:
[tex]\[ 4, 8, 8, 6 \][/tex]
Here, [tex]\( 8 \)[/tex] appears twice as an [tex]\( x \)[/tex]-value. This means the input [tex]\( 8 \)[/tex] is associated with more than one output. Therefore, this set does not represent a function.
After analyzing each set, we conclude that the set [tex]\(\{(4, 1), (8, 2), (8, 7), (6, -2)\}\)[/tex] does not represent a function because it has repeated [tex]\( x \)[/tex]-values (specifically, [tex]\( 8 \)[/tex] appears twice).
Therefore, the correct answer is:
[tex]\[
\{(4,1),(8,2),(8,7),(6,-2)\}
\][/tex]
