Check relations from pairs and mapping tables quickly. Spot repeated inputs and compare output values. Get clear answers, classifications, and exportable reports for practice.
A relation is a function when one input never has two different outputs.
Function test: If (x, y1) and (x, y2) are both listed, then y1 must equal y2.
One-to-one test: If f(x1) = f(x2), then x1 must equal x2.
Onto test: Range = Codomain.
Complete on supplied domain: Every listed domain value appears as an input exactly once after conflict checking.
Many-to-one test: Two different inputs can share one output while the relation still remains a function.
| Case | Pairs | Domain | Codomain | Result |
|---|---|---|---|---|
| Linear Mapping | (1,2), (2,4), (3,6) | 1, 2, 3 | 2, 4, 6 | Bijective function |
| Shared Output | (1,5), (2,5), (3,7) | 1, 2, 3 | 5, 7 | Many-to-one function |
| Conflict Example | (2,4), (2,6), (3,9) | 2, 3 | 4, 6, 9 | Not a function |
A function connects each input to one output. That rule is strict. A repeated input cannot produce two different outputs. This calculator checks that rule first. It then gives deeper classifications when your sets are supplied.
Many students first watch the outputs. That can confuse the result. The main test starts with inputs. If input 4 goes to 9 and 11, the relation fails. It is not a function. Shared outputs do not automatically break the rule.
A relation can send different inputs to the same output. That pattern is many-to-one. It is still a function because each input keeps one answer. For example, 1 to 5 and 2 to 5 is allowed. The calculator marks that case clearly.
One-to-one functions are special. They never repeat an output for different inputs. These functions are easier to reverse. They matter in algebra and inverse work. The tool checks that pattern by comparing outputs across all valid inputs.
The codomain gives the full target set. A function is onto when every codomain value appears in the range. This matters in set theory and formal mapping questions. If some codomain values stay unused, the tool reports them in the notes section.
Sometimes a teacher gives a full domain. Then you must verify complete coverage. Every listed input should appear in the relation. The calculator compares your entered pairs with the supplied domain. It shows missing inputs and extra inputs outside the stated set.
The result area is built for review. It shows the relation domain, range, mapping table, and classification. Conflicts are listed one by one. Ignored lines are also shown. That makes it easier to correct typing mistakes and learn the rule behind the answer.
Teachers often ask students to judge a relation from a table. Small typing errors can hide the real pattern. This tool reduces that problem. It separates valid lines from ignored lines. It also lists every conflict directly. That helps with homework checking, quiz review, and independent practice. Very clearly. It supports faster revision before tests too.
A relation is a function when each input has exactly one output. Repeated outputs are allowed. Repeated inputs with different outputs are not allowed.
Yes. That is called many-to-one. It still counts as a function because each input keeps only one assigned output.
A one-to-one function gives different outputs for different inputs. No output is shared by two distinct inputs. These functions can have inverses more easily.
Onto means every value in the supplied codomain is used by the function. If one codomain value is missing, the function is not onto.
Lines are ignored when they do not match a supported pair format. Use one pair per line and separate values with a comma, arrow, or colon.
Yes. You can enter values like A, B, cat, or red. Use the case sensitivity option when uppercase and lowercase should be treated differently.
Domain coverage matters when a question gives a full starting set. A complete function on that set must include every listed input.
Yes. After calculation, you can download a CSV file or a PDF summary. Both exports include the main decision and table data.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.