Question

Which of the following pairs represent a function ​

Answer 1

Option D: $\{(-9,8),(-5,-8),(-7,8),(-6,-8)\}$ 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: $\{(-12,8),(-15,8),(-5,-8),(-12,-8)\}$

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 $\{(-12,8),(-15,8),(-5,-8),(-12,-8)\}$ is not a function.

Hence, Option A is not the correct answer.

Option B: $\{(8,-9),(-8,-5),(8,-7),(-8,-6)\}$

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 $\{(8,-9),(-8,-5),(8,-7),(-8,-6)\}$ is not a function.

Hence, Option B is not the correct answer.

Option C: $\{(13,-3),(13,0),(13,-1),(13,-1)\}$

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 $\{(13,-3),(13,0),(13,-1),(13,-1)\}$ is not a function.

Hence, Option C is not the correct answer.

Option D: $\{(-9,8),(-5,-8),(-7,8),(-6,-8)\}$

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 $\{(-9,8),(-5,-8),(-7,8),(-6,-8)\}$ is a function.

Hence, Option D is the correct answer.