In this Section:
In this section, we continue to learn about the idea of a function. Here, we will focus on methods to determine if a relation is that of a function. One such method is known as the vertical line test. The vertical line test begins with graphing of the given relation. Once this is complete, we inspect the graph to see if any vertical line would intersect the graph in more than one place. If any vertical line touches the graph in more than one place, the graph represents a relation that is not a function. If no vertical line would ever touch the graph in more than one place, the relation is in fact a function. For an explanation of this concept, we can think back to when we graphed vertical lines: x = k. For these lines, we find the given x value on our coordinate plane, and sketch a vertical line. Knowing this, we can say if a vertical line intersects a given graph in more than one location, it violates the definition of a function. For that given x value, there exists more than one y value.