When is an ordered pair a function

There can be at most one output for every input. The inputs that make "sense" form the domain of the function, and the answers or outputs form the range. We can call the input x , the rule f , and then the output is f x , read " f of x ". Note: f 3 is not f times 3. A function is a special type of relation. A relation is just a set of ordered pairs x , y.

In formal mathematical language, a function is a relation for which:. This just says that in a function, you can't have two ordered pairs with the same x -value but different y -values. If you have the graph of a relation, you can use the vertical line test to find out whether the relation is a function. Names of standardized tests are owned by the trademark holders and are not affiliated with Varsity Tutors LLC.

Media outlet trademarks are owned by the respective media outlets and are not affiliated with Varsity Tutors. Functions are relations that derive one output for each input, or one y-value for any x-value inserted into the equation. For example, the equations:.

In graphical terms, a function is a relation where the first numbers in the ordered pair have one and only one value as its second number, the other part of the ordered pair. For example.

Equations with exponents can also be functions. For example:. Determining whether a relation is a function on a graph is relatively easy by using the vertical line test. If a vertical line crosses the relation on the graph only once in all locations, the relation is a function. However, if a vertical line crosses the relation more than once, the relation is not a function.

Using the vertical line test, all lines except for vertical lines are functions. Circles, squares and other closed shapes are not functions, but parabolic and exponential curves are functions. An input-output chart displays the output, or result, for each input, or original value. Any input-output chart where an input has two or more different outputs is not a function. For example, if you see the number 6 in two different input spaces, and the output is 3 in one case and 9 in another, the relation is not a function.

However, if two different inputs have the same output, it is still possible that the relation is a function, especially if squared numbers are involved. Daniel Pinzow served as an urban science teacher for several years.