The Vertical Line Test
The test states that a graph represents a function if and only if all vertical lines intersect the graph at most once.
This graph does not represent a function: for example, the vertical line
intersects it in three places.
This graph does represent a function, since any vertical line intersects the graph exactly once, except
which doesn't intersect it at all.
Consider the graph shown.
You can see that no vertical lines pass through two points on the graph.
Note that and are open points and are not on the graph. So, the vertical lines and pass through only one point on each of the line segments.
Therefore, the graph shown is of a function.
The step function can be defined as:
The domain of the function is and the range is .