Relation and Function for School Maths Lab

Quick Answer: Relation and Function is a mapping model for teaching the difference between a relation, any set of pairings between two sets, and a function, in which each element of the first set is paired with exactly one element of the second. Students use the relation and function model to identify domain, codomain and range.

Arrows Between Two Sets

Arrow diagrams are the standard way to introduce relations. Elements of set A sit on the left, elements of set B on the right, and an arrow from a to b means the ordered pair (a, b) belongs to the relation. A physical mapping model makes the arrows movable, so the class can change one connection and ask at once whether the relation is still a function.

The test is simple to state: every element of A must have exactly one arrow leaving it. If an element has no arrow, or has two, the relation is not a function from A to B. Several elements of A may point to the same element of B, which is allowed. The set A is the domain, B is the codomain, and the elements of B that actually receive arrows form the range.

Senior classes extend the same picture to one-one functions, where no two arrows arrive at the same element of B, and onto functions, where every element of B receives at least one arrow. How the sets and connections are represented on this model, whether by strings, pegs or cards, should be confirmed at enquiry.

Applications

• Showing a relation both as a set of ordered pairs and as an arrow diagram
• Testing whether a relation is a function by counting the arrows leaving each element
• Identifying the domain, codomain and range of a given mapping
• Classifying functions as one-one, onto or both

Specifications

Care & Handling

• Keep the connecting pieces in a bag attached to the board so none are lost between lessons.
• If strings or elastic bands are used, untangle them and return them to their start positions after use.
• Wipe the board with a dry cloth and avoid markers that stain.

Why Choose LabEquip

Teachers who begin Class 11 with sets often use the Set Theory By Venn Diagram model first and this mapping model next, since relations are built from ordered pairs of set elements, and the Graph Board then shows the same functions as graphs. LabEquip supplies all three from its maths lab range.

Frequently Asked Questions

What is the difference between a relation and a function?

A relation from A to B is any set of ordered pairs (a, b) with a in A and b in B. A function is a special relation in which every element of A appears in exactly one pair. So every function is a relation, but many relations are not functions.

What are domain, codomain and range?

The domain is the set of inputs, A. The codomain is the set B from which outputs are allowed to come. The range is the set of outputs actually used, which is part of the codomain and may be smaller than it.

Can two elements of the domain map to the same element?

Yes. A function allows many-to-one mappings, such as squaring, where 2 and −2 both map to 4. What it does not allow is one-to-many, where a single input has two different outputs.

What is a one-one function?

A function is one-one, or injective, if different inputs always give different outputs. On an arrow diagram, no element of the codomain receives more than one arrow. On the real numbers, f(x) = 2x + 1 is one-one, while f(x) = x² is not.

How many relations are there from a set with 2 elements to a set with 3 elements?

The Cartesian product A × B has 2 × 3 = 6 ordered pairs, and any subset of it is a relation, so there are 2⁶ = 64 relations. Only 3² = 9 of them are functions from A to B, because each of the 2 elements picks one of 3 images.

What is the vertical line test?

When a relation between real numbers is drawn as a graph, it is a function of x if no vertical line crosses the graph more than once. A circle fails the test, since a vertical line through its interior meets it twice, while the parabola y = x² passes.

Last Updated: September 2026