In this section, you will find the basics of the topic – definition of functions and relations, special functions, different types of relations and some of the solved examples. What is a Function?

Relations and functions define a mapping between two sets. A relation is defined as the set of ordered pairs whereas a function is a special type of relation where every element of domain is mapped to exactly one element of the codomain.

Apr 7, 2025 · Learn what functions are, their types, properties, and how they map inputs to outputs with real-life examples and mathematical operations. Explore key differences between relations and functions and see how they appear in real-world situations. Practice and test your understanding with quizzes and problems on relations and functions.

In mathematics, a function can be defined as a rule that relates every element in one set, called the domain, to exactly one element in another set, called the range. For example, y = x + 3 and y = x 2 – 1 are functions because every x-value produces a different y-value. A relation is any set of ordered-pair numbers.

In these examples, we see that when we say “ a a is related to b b,” the order in which a a and b b appear may make a difference. This suggests the following definition. A relation from a set A A to a set B B is a subset of A × B A × B. Hence, a relation R R consists of ordered pairs (a, b) (a, b), where a ∈ A a ∈ A and b ∈ B b ∈ B.

Apr 21, 2025 · In the context of algebra, the relations of interest are sets of ordered pairs \((x, y)\) in the rectangular coordinate plane. In this case, the \(x\)-values define the domain and the \(y\)-values define the range. Of special interest are relations where every \(x\)-value corresponds to exactly one \(y\)-value; these relations are called functions.

In mathematics, understanding the concept of relations is essential before diving into functions. Let's start by defining a relation and then explore how it connects to a function.

Learn about ordered-pair numbers, relations and an introduction to functions, Algebra: What are relations and functions, How to determine whether a relation is a function, how to use a mapping and the vertical line test, how to work with function notation, with video lessons, examples and step-by-step solutions.

4 days ago · Determining Whether a Relation Represents a Function. A relation is a set of ordered pairs. The set of the first components of each ordered pair is called the domain and the set of the second components of each ordered pair is called the range.. Consider the following set of ordered pairs.\[ \{ (1,2), (2,4), (3,6), (4,8), (5,10) \} \nonumber \]The first numbers in …

Introduction to functions: Difference between an “equation” and a “function:” Khan Academy on functions: Functions. A relation is a set of ordered pairs, where the set of first components in the ordered pair is called the domain, and the set of second components is called the range.