Explain how a graph fails the vertical line test.
if a vertical line can be drawn which crosses the graph at more than one point
... the graph fails the vertical line test
Sure! The vertical line test is a useful tool for determining whether a graph represents a function or not. In order to pass the vertical line test, a graph must have the property that no vertical line can intersect the graph in more than one place.
So, how can a graph fail the vertical line test? If there exists at least one vertical line that intersects the graph at two or more distinct points, then it fails the vertical line test and does not represent a function.
To visually check whether a graph fails the vertical line test, follow these steps:
1. Draw a vertical line anywhere on the graph. You can imagine sliding the line from left to right or right to left.
2. Observe whether the vertical line intersects the graph at more than one point. If it does, the graph fails the vertical line test.
For example, consider a graph of a circle. A circle fails the vertical line test because if you imagine sliding a vertical line across the graph, it will intersect at two or more distinct points along the perimeter of the circle.
In summary, a graph fails the vertical line test when a vertical line intersects the graph at more than one point, indicating that it does not represent a function.