Question

Which of the relations given by the following sets of ordered pairs is a function?a. {(1, 1), (1, 3), (1, 5), (1, 7), (1, 9)}b. {(-2, 1), (7, 5), (-4,0),(3,1),(0,-6)}c. {(1,2),(2,3),(3,4), (3,3),(2,2),(1,1)}d. {(2, -7), (6,5),(-3,9), (2,0), (-5,3)}

Answer 1

Option B) {(-2, 1), (7, 5), (-4,0),(3,1),(0,-6)} is correct.

Explanation:

Consider the provided information.

According to function definition: a relationship between a set of inputs and a set of possible outputs in which each input is connected to exactly one output.

Now consider the provided options:

Option A) {(1, 1), (1, 3), (1, 5), (1, 7), (1, 9)}

Here, 1 is not connected to exactly one output.

For example 1 is connected with 1, 3, 5, 7 and 9.

Thus, it is not the correct option.

Option B) {(-2, 1), (7, 5), (-4,0),(3,1),(0,-6)}

Here, each input is connected to exactly one output.

Thus, option B is correct.

Option C) {(1,2),(2,3),(3,4), (3,3),(2,2),(1,1)}

Here, 1, 2 and 3 are not connected to exactly one output.

For example 1 is connected with 1, and 2, similarly 2 is connected with 2 and 3.

Thus, it is not the correct option.

Option D) {(2, -7), (6,5),(-3,9), (2,0), (-5,3)}

Here, 2 is not connected to exactly one output.

2 is connected with -7, and 0.

Thus, it is not the correct option.

Hence, Option B) {(-2, 1), (7, 5), (-4,0),(3,1),(0,-6)} is correct.