Question

Is this a relation: {(-2,1), (0,0), (0,1), (1,-2), (1,0), (1,3), (2,0)}? Explain why or why not.

Answer 1

It is a relation because any relation is simply a set of (x,y) values known as points or ordered pairs. There are no other qualifications needed to be a relation. We simply pair up any x and y value we want.

I think you meant to ask if it's a function or not. If so, then the answer is "no, it is not a function". Why not? Because the x value x = 0 produces more than one y output y = 1 and y = -2. Graph these points and you'll see them fail the vertical line test (ie its possible to draw a vertical line through more than one point on the graph). The same issue happens with (1,-2), (1,0) and (1,3) as well.

In summary:

Yes it is a relation

No it is not a function

The reasoning for each is stated above