Question

For what value of c is the relation a function (2,8),(12,3),(c,4),(-1,8),(0,3)

Answer 1

Answer: Its 1

Explanation:

( x is always the first number of the pairs and y is the second)

{( 2 , 8 ) , ( 12 , 3 ) , ( c , 4 ) , ( - 1 , 8 ) , ( 0 , 3 ) }

Now Look At The Answers : -1 , 1 , 2 , 12

(x will always only have one partnering number otherwise it wouldn’t qualify as a function.)

Notice how the answer “2” is in the first number pair? That means it can’t be 2 because it is already paired up with y (aka 8).
Now Look At The Answers : -1 , 1 , 12

If you continue to go through the pairs and the answers you will see that there is only one remaining number. And that’s “1”

Answer 2

The value of c is { c | c ∈ R, c ∉ {-1,0,2,12} }.
c is a number such that it is not in the set {-1,0,2,12} else we end up with a domain value having multiple range values, contradicting with the definition of a function.