Question

Which of the sets of ordered pairs represents a function?

A = {(1, −2), (3, −5), (5, 2), (7, 5)}

B = {(4, 2), (4, −2), (9, 3), (9, −3)}


only A
only B
Both A and B
neither A or B

Answer 1

It's only A, because for each x, there's only one y, unlike B where there are two values for x=4 and two for x=9.

Answer 2

Option A is correct.

only set A is the ordered pairs represents a function.

Explanation:

By the definition of a function, for each input there exists a unique output.

In particular, for each value of x there exists unique value of y.

In set A,

we have four ordered pair (1, -2) , (3, -5) , (5, 2) and (7, 5)

For each input value of x in set A, there is a unique value of y in set A.

therefore, Set A is a function.

In set B,

we have four ordered pair (4, 2) , (4, -2), (9, 3) and (9, -3)

which means for x=4 , we have two values of y, i.,e 2 and -2

⇒ for a single value of x , there exist more than one value of y,

therefore set B is not a function