Question

Explain what the vertical line test is and how it is used.

Answer 1

A test used to determine if a relation is a function. A relation is a function if there are no vertical lines that intersect the graph at more than one point.

Answer 2

The vertical line test is a test to determine if a relation or its graph is a function or not. For a relation or graph to be a function, it can have at most a single y-value for each x-value. Thus, a vertical line drawn at any x-position on the graph of a function will intersect the graph at most once. 

To use the vertical line test graphically, take a ruler or other "vertical line" and move it from one end of the x-axis to the other while keeping it parallel to the y-axis. If the graph intersects the ruler or vertical line more than once at any given value of y, the graph is not a function. However, if the graph intersects the vertical line no more than once at any given point, it is a function.