How to use this calculator

To test a relation given as ordered pairs, check whether any input is associated with more than one distinct output. Multiple inputs can share the same output. This calculator groups inputs, lists unique domain and range values, and plots the relation.

The method

A relation is a function when every x has exactly one y

Enter the values in the labeled fields, check the units or selected mode, and choose Calculate. The result includes the applicable working and a breakdown or visual when useful. Change an input and calculate again to update the result.

WORKED EXAMPLE

Ordered pairs: 1,2; 2,4; 3,4

Is this relation a function?: Yes, it is a function

A function assigns exactly one output to each input.

Scope and limitations

Up to 100 coordinate pairs. Identical repeated pairs are accepted. The test applies only to the listed pairs, not to an inferred curve between them.

Common questions

Can two points have the same y-value?

Yes. A function may assign the same output to different inputs.

Do duplicate pairs make it fail?

No. Repeating exactly the same pair does not assign a new output to that input.

References & further reading

External references provide background, not an endorsement of this implementation. See our methodology for numerical conventions and limitations.