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
. 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.