Question

Each answer choice below represents a relation by a set of ordered pairs. In which of the answer choices is the relation a function? Select all correct answers. Select all that apply:

{(8,12),(−3,0),(1,0),(−1,13)}

{(1,9),(4,2),(3,−3),(4,−2)}

{(−1,8),(−1,12),(−2,13),(5,−1)}

{(−4,12),(0,−3),(3,5),(−2,−3)}

{(1,0),(4,4),(−4,9),(−2,9)}

Answer 1

Options (1), (4) and (5) are the functions.

Explanation:

Option (1)

In the given set of ordered pairs, for every input value there is a y-value which is either different or same.

They represent a many to one function.

Option (2)

In the given set of ordered pairs (4, 2) and (4, -2) represent different y-values for the same x-values.

Therefore, they don't represent a function.

Option (3)

Ordered pairs (-1, 8) and (-1, 12) show the different output values for same input values.

Therefore, this set doesn't represent a function.

Option (4)

In the given set of ordered pairs, for every input value there is a y-value which is either different or same.

They represent a many to one function.

Option (5)

In the given set of ordered pairs, for every x- value there is a y-value which is either different or same.

They represent a many to one function.