Question

Use the domain and range of each of the following relations to determine which is a function. A. {(–4, 3), (–2, –1), (–4, 8)} B. {(–4, 3), (–2, –1), (–7, 8)} C. {–4, –2, –7, 7} D. {(–4, 3), (–2, –1), (–2, –8), (–7, 8)}

Answer 1

Answer:

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

$R=\{(x,y),x\in R,y\in R\}$

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.