Option B and Option C.
Step-by-step explanation:
A relation is a function if there exist a unique output for each input.
If a relation is defined as
then relation R is a function if there exist a unique value of y for each value of x.
In option A, the given relation is
{(–4, 3), (–2, –1), (–4, 8)}
Domain = {-4,2}
Range = {3,-1,8}
It is not a function because at x=-4 we have more than one output value, y=3 and y=8.
In option B, the given relation is
{(–4, 3), (–2, –1), (–7, 8)}
Domain = {-4,-2,-7}
Range = {3,-1,8}
It is a function.
In option C, the given relation is
{(–4, –2), (–7, 7)}
Domain = {-4,-7}
Range = {-2,7}
It is a function.
In option D, the given relation is
{(–4, 3), (–2, –1), (–2, –8), (–7, 8)}
Domain = {-7,-4,-2}
Range = {-8,-1,3,8}
It is not a function because at x=-2 we have more than one output value , y=-1 and y=-8.
Therefore, the correct options are B and C.