To determine which set of ordered pairs represents a function, we need to ensure that for each [tex]\( x \)[/tex]-value, there is only one corresponding [tex]\( y \)[/tex]-value. In other words, no [tex]\( x \)[/tex]-value should be associated with more than one [tex]\( y \)[/tex]-value.
Let's evaluate each set of ordered pairs one by one:
### Set 1: [tex]\(\{(9,8),(-6,-9),(1,-9),(1,1)\}\)[/tex]
- The [tex]\( x \)[/tex]-values are [tex]\( 9, -6, 1, 1 \)[/tex].
- The [tex]\( x \)[/tex]-value 1 appears twice with different [tex]\( y \)[/tex]-values: [tex]\((1, -9)\)[/tex] and [tex]\((1, 1)\)[/tex].
Since the [tex]\( x \)[/tex]-value 1 is associated with more than one [tex]\( y \)[/tex]-value, this set does not represent a function.
### Set 2: [tex]\(\{(9,5),(-7,-8),(6,-8),(4,-1)\}\)[/tex]
- The [tex]\( x \)[/tex]-values are [tex]\( 9, -7, 6, 4 \)[/tex].
- Each [tex]\( x \)[/tex]-value appears only once and is associated with a unique [tex]\( y \)[/tex]-value.
Since each [tex]\( x \)[/tex]-value has a unique corresponding [tex]\( y \)[/tex]-value, this set represents a function.
### Set 3: [tex]\(\{(8,7),(2,-4),(2,0),(-8,-9)\}\)[/tex]
- The [tex]\( x \)[/tex]-values are [tex]\( 8, 2, 2, -8 \)[/tex].
- The [tex]\( x \)[/tex]-value 2 appears twice with different [tex]\( y \)[/tex]-values: [tex]\((2, -4)\)[/tex] and [tex]\((2, 0)\)[/tex].
Since the [tex]\( x \)[/tex]-value 2 is associated with more than one [tex]\( y \)[/tex]-value, this set does not represent a function.
### Set 4: [tex]\(\{(6,-9),(-8,5),(6,1),(8,-3)\}\)[/tex]
- The [tex]\( x \)[/tex]-values are [tex]\( 6, -8, 6, 8 \)[/tex].
- The [tex]\( x \)[/tex]-value 6 appears twice with different [tex]\( y \)[/tex]-values: [tex]\((6, -9)\)[/tex] and [tex]\((6, 1)\)[/tex].
Since the [tex]\( x \)[/tex]-value 6 is associated with more than one [tex]\( y \)[/tex]-value, this set does not represent a function.
### Conclusion:
Among the given sets, only the second set [tex]\(\{(9,5),(-7,-8),(6,-8),(4,-1)\}\)[/tex] represents a function.
