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:
{(6,12),(3,1),(−1,13),(6,4)}

{(−1,−2),(−4,−4),(0,−5),(7,−5)}

{(−5,1),(4,10),(5,10),(6,7)}

{(−1,4),(1,6),(−1,−2),(0,7)}

{(−2,8),(2,1),(−4,8),(7,9)}

Answer 1

Answer:

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.