Option D: [tex]\{(-9,8),(-5,-8),(-7,8),(-6,-8)\}[/tex] are the ordered pairs represents a function.
Explanation:
Given that the options of the set of ordered pairs.
We need to determine the ordered pairs that represents a function.
Option A: [tex]\{(-12,8),(-15,8),(-5,-8),(-12,-8)\}[/tex]
A relation is said to be a function if each element of x is related to exactly one element in y.
From this set of ordered pairs, it is obvious that the element -12 of x is related to two different element in y.
Thus, the ordered pairs [tex]\{(-12,8),(-15,8),(-5,-8),(-12,-8)\}[/tex] is not a function.
Hence, Option A is not the correct answer.
Option B: [tex]\{(8,-9),(-8,-5),(8,-7),(-8,-6)\}[/tex]
From this set of ordered pairs, it is obvious that the elements -8 and 8 of x are related to two different element in y.
Thus, the ordered pairs [tex]\{(8,-9),(-8,-5),(8,-7),(-8,-6)\}[/tex] is not a function.
Hence, Option B is not the correct answer.
Option C: [tex]\{(13,-3),(13,0),(13,-1),(13,-1)\}[/tex]
From this set of ordered pairs, it is obvious that the element 13 of x is related to three different element in y.
Thus, the ordered pairs [tex]\{(13,-3),(13,0),(13,-1),(13,-1)\}[/tex] is not a function.
Hence, Option C is not the correct answer.
Option D: [tex]\{(-9,8),(-5,-8),(-7,8),(-6,-8)\}[/tex]
A relation is said to be a function if each element of x is related to exactly one element in y.
From this set of ordered pairs, it is obvious that the each element of x is related exactly one element in y.
Thus, the ordered pairs [tex]\{(-9,8),(-5,-8),(-7,8),(-6,-8)\}[/tex] is a function.
Hence, Option D is the correct answer.
