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.

Step-by-step 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.