Question

Match the ordered pairs so that the relation defined by the set of ordered palrs does not represent a function.

(2,3)
(-5,2)
(-5, 1)
(6,-5)
(6,5)
|(2, 2)
(0,3)
(-1,0)
(-1,6)
I I I
​

Answer 1

Here is the result:

(2, 3) ↔ (2, 2) ∵ x = 2 is duplicated

(-5, 2) ↔ (-5, 1) ∵ x = -5 is duplicated

(6, -5) ↔ (6, 5) ∵ x = 6 is duplicated

(-1, 0) ↔ (-1, 6) ∵ x = -1 is duplicated

Here, each matching pair has duplicated input values, so neither of them represents the function.

Explanation:

We know that a function is a relation where each input or x-value of the X set has a unique y-value or output of the Y set.

In other words, we can not have duplicated inputs as there should be only 1 output for each input.

We are given that we need to match the ordered pairs so that the relation defined by the set of ordered pairs does not represent a function.

Therefore, all we need is to match the ordered pairs which have the same input value as it would violate the relation to be function.

Here is the result:

(2, 3) ↔ (2, 2) ∵ x = 2 is duplicated

(-5, 2) ↔ (-5, 1) ∵ x = -5 is duplicated

(6, -5) ↔ (6, 5) ∵ x = 6 is duplicated

(-1, 0) ↔ (-1, 6) ∵ x = -1 is duplicated

Here, each matching pair has duplicated input values, so neither of them represents the function.