Option D:
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: ![\{(-12,8),(-15,8),(-5,-8),(-12,-8)\}](https://tex.z-dn.net/?f=%5C%7B%28-12%2C8%29%2C%28-15%2C8%29%2C%28-5%2C-8%29%2C%28-12%2C-8%29%5C%7D)
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
is not a function.
Hence, Option A is not the correct answer.
Option B: ![\{(8,-9),(-8,-5),(8,-7),(-8,-6)\}](https://tex.z-dn.net/?f=%5C%7B%288%2C-9%29%2C%28-8%2C-5%29%2C%288%2C-7%29%2C%28-8%2C-6%29%5C%7D)
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
is not a function.
Hence, Option B is not the correct answer.
Option C: ![\{(13,-3),(13,0),(13,-1),(13,-1)\}](https://tex.z-dn.net/?f=%5C%7B%2813%2C-3%29%2C%2813%2C0%29%2C%2813%2C-1%29%2C%2813%2C-1%29%5C%7D)
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
is not a function.
Hence, Option C is not the correct answer.
Option D: ![\{(-9,8),(-5,-8),(-7,8),(-6,-8)\}](https://tex.z-dn.net/?f=%5C%7B%28-9%2C8%29%2C%28-5%2C-8%29%2C%28-7%2C8%29%2C%28-6%2C-8%29%5C%7D)
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
is a function.
Hence, Option D is the correct answer.