What is explain what the vertical line test is and how it is used.?

The Vertical Line Test is a visual method used to determine whether a curve plotted on a graph represents a function.

How it works:

1. Draw a vertical line anywhere on the graph.
2. Observe the number of times the vertical line intersects the curve.
3. If the vertical line intersects the curve at only one point, then the curve represents a function.
4. If the vertical line intersects the curve at more than one point, then the curve does not represent a function.

Why it works:

The definition of a function requires that for each input (x-value), there is only one output (y-value). When a vertical line intersects a curve at more than one point, it means that for a single x-value, there are multiple y-values. This violates the definition of a function. Conversely, If each x value in the domain has only one y value as its corresponding range, then it is a function.

Example:

• A straight line (that is not vertical) will always pass the vertical line test because any vertical line will only intersect it once.
• A circle will fail the vertical line test because a vertical line through the center of the circle (and others) will intersect it twice. Thus a circle does not represent a function.