Question

Which of the following sets represents a function?

A. {(3, 5), (-1, 7), (3, 9)}
B. {(1, 2), (3, 2), (5, 7)}
C. {(1, 2), (1, 4), (1, 6)}

Answer 1

A function is a special relationship where each input has a single output.

A. The set {(3, 5), (-1, 7), (3, 9)} doesn't represent a function, because input x=3 has two outputs
`y_1=5` and
`y_2=9.`

C. The set {(1, 2), (1, 4), (1, 6)} doesn't represent a function, because input x=1 has three outputs
`y_1=2,`
`y_2=4` and
`y_3=6.`

B. The set {(1, 2), (3, 2), (5, 7)} represents a function, because each input has a single output.

Answer: correct choice is B.

Answer 2

A data set can be verified to be a function or not through the vertical line test. In this test, if the data set has points lying on the same vertical line, then it is not a function. This means the points should not have the same x. The answer hence to the problem is B.