The Vertical Line Test & Alternative Definitions of Function
The vertical line test is a way of determining whether the graph of a relation is the graph of a function.
Vertical Line Test
If every vertical line intersects the graph of a relation in no more than one point, then the relation is a function.
Take a look at this short video for some examples:
Understanding the vertical line test leads to the following alternative definitions of a function.
Alternative Definitions of Function
- A function is a relation in which, for each distinct value of the first component of the ordered pairs, there is exactly one value of the second component.
- A function is a set of ordered pairs in which no first component is repeated.
- A function is a rule or correspondence that assigns one range value to each distinct domain value.