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In mathematics, a relation is a set of ordered pairs, where each ordered pair consists of two elements, typically referred to as the x-coordinate (×) and the y-coordinate (y). A relation can be thought of as a collection of points on a coordinate plane.

On the other hand, a function is a special type of relation where each x-coordinate is associated with only one y-coordinate. In other words, no two ordered pairs in a function have the same x-coordinate but different y-coordinates.

Let's analyze the given ordered pairs: (1,2), (5,3), (5,-2), (3,6), (10,15), and (7,0).

If we examine the x-coordinates, we can see that there are no repeated x-values. Each value appears only once: 1, 5, 3, 10, and 7.

Therefore, to determine whether the given relation is a function, we need to check if there are any repeated x-coordinates with different y-coordinates.

In this case, we can see that no two ordered pairs have the same x-coordinate but different y-coordinates. Each x-coordinate is associated with a unique y-coordinate. Hence, the given relation is a function.
 

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