Determine which relation is a function.

Hello!

In a function, each input has one output. Therefore, each x value on the graph should only have one y value on it, So, for example on graph A, The vertical line has infinite points on one x value, so it is absolutely not a function.

A good way to test whether a graph is a function is the vertical line test. What you do is imagine an invisible vertical line going across the graph. If at any point this vertical line hits two points of the graph, it is not a function.

For example, in graph B, if you move the vertical line across, it will hit the ellipse twice; on the top edge and the bottom. In C, a vertical line will intersect with the circle twice. 

To make that a bit more clear, in C, if you put a vertical line down the middle, it will intersect at  both the points (0,2) and (0,-2).

In D, you can put down the vertical line anywhere and it will not intersect with two points on the graph, therefore D is a function and our answer.

I hope this helps!