Which of the following relations is a function?
A. (2, 4), (-4, 6), (2, 3), (-7, 2)

B. (6, 1), (-4, 4), (2, 1), (6, 2)

C. (2, 4), (-4, 2), (6, 1), (-7, 2)

D. (2, 0), (-4, 3), (6, 1), (-4, 5)

Question

Which of the following relations is a function?
	A. 	 (2, 4), (-4, 6), (2, 3), (-7, 2)

	B. 	 (6, 1), (-4, 4), (2, 1), (6, 2)

	C. 	 (2, 4), (-4, 2), (6, 1), (-7, 2)

	D. 	 (2, 0), (-4, 3), (6, 1), (-4, 5)

anonymous · Answer

A relation is a function when it connects a unique value of x to a value of y. That means, you cannot have the same value of x mapped to different values of y. Putting a particular value of x should direct you towards a single value of y. Going by this, you can probably eyeball that only C is the relation which is  a function. You can check for yourself.

anonymous · Answer

You can see that in A, B and D the same value of x has more than one value of y. You don't want that for a function. A function should direct you to a single value of y for a value of x.

whpalmer4 · Answer

Right, and @silversurfer  makes an important distinction which is often overlooked.  It is okay to have the same x value appear multiple times in the list if (and only if) it always has the same y value associated with it.  Some posters say if the x value is repeated, that means the relation is not a function; that is overly simplistic, and incorrect.  The correct test is that if any single value of x has multiple associated values of y, the relation is not a function.