# Given the below represent the relation as a set of ordered pairs a graph and as a map x -1 0 3 y 1 -2 5

###### Question:

## Answers

A - Not Function

B - Function

C - Function

D - Not Function

E - Function

Step-by-step explanation:

For a relation to be a function, each value of input should have exactly one output. Which means that for one value of x, there should only one value of y. If the relation has repetition of x in its ordered pairs, it means that for one value of x, there are two or more values of y, hence the relation is not a function

(Consult the diagram below)

A - {(6,12),(3,1),(−1,13),(6,4)}As x = 6 is being repeat, it means that x=6 has two values of y that are 12 and 4. IT IS NOT A FUNCTION.

B - {(−1,−2),(−4,−4),(0,−5),(7,−5)}No repetition of x, IT IS A FUNCTION.

C - {(−5,1),(4,10),(5,10),(6,7)}No repetition of x, IT IS A FUNCTION.

D - {(−1,4),(1,6),(−1,−2),(0,7)}As x = -1 is being repeat, it means that x=-1 has two values of y that are 4 and -2. IT IS NOT A FUNCTION.

E - {(−2,8),(2,1),(−4,8),(7,9)}No repetition of x, IT IS A FUNCTION.

[tex]Each answer choice below represents a relation by a set of ordered pairs. In which of the answer cho[/tex]

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

Step-by-step 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.

{(−5,−3),(−3,2),(3,3),(9,3)}

{(−5,−3),(6,−4),(9,−5),(−2,−5)}

{(7,−1),(4,7),(0,−1),(2,14)}

Step-by-step explanation:

These 3 answer choices all represent functions since the x-values only correspond to one y-value.

The other answer choices are not functions because some of the x-values correspond to more than one y-value.