Question

Which of the following sets of ordered pairs represents a function?

A.
{(-12,8), (-15,8), (-5,-8), (-12,-8)}
B.
{(8,-9), (-8,-5), (8,-7), (-8,-6)}
C.
{(13,-3), (13,0), (13,-1), (13,-1)}
D.
{(-9,8), (-5,-8), (-7,8), (-6,-8)}

Answer 1

D.

{(-9,8), (-5,-8), (-7,8), (-6,-8)}

Explanation:

A function is defined as the relation between two sets with an specific characteristic:

• If each x-value has only one y-value assigned, then the expression it's a function.
• If each x-value has more than one y-value image, then the expression it's not a function, it's just a relation.

So, in this problem, we have to look for this characteristic. Option A has two points with the same x-value and different y-value assigned, so it's not a function. Option B has two y-values assigned for x=8, so it's not a function either. Option C is not a function because x=13 has to different images y=-3 and y=0.

At last, option D represent a function, because each x-value has only one image: {(-9,8), (-5,-8), (-7,8), (-6,-8)}

It's important to notice that, one y-value can have different x-values assigned, that's a function, but it cannot happen in the opposite way, one x-value with more than one y-value assigned.

Therefore, the right answer is D.