# Differences between function and relationship in math’s

Function and relation are two different mathematical terms. To understand what differentiates them, we must know the concepts that define them.

## What is a Function?

In mathematics, one quantity or quantity is a function of another if the value of the first depends on the second. For example, the area A of a circle is a function of its radius, or the duration T of a trip is a function of distance and speed. In this case, area and time are dependent variables, and radius, speed, and distance are independent variables.

In mathematical analysis, a function is a rule that assigns to each element of a first set a single element of a second set.

A function can be represented in various ways, using an algorithm or equations, using tables of values that match the independent variable with the dependent variable, or as graphs that give a picture of the function.

## What is a Relationship?

A mathematical relationship involves the idea of correspondence between the elements of two sets that form pairs. When an expression is formulated, two or more objects are related to each other and a relationship is postulated that is not necessarily mathematical.

In a mathematical relationship, we find the correspondence that exists between two sets. Each element of the first set corresponds to at least one of the second set.

## Differences between function and relationship

- When each element of a set corresponds only to one of the other, we speak of a function. Mathematical functions are always relations. However, not all relationships are always function.
- In a relationship, the first set is called the domain and the second set is called the range. They are graphed on the Cartesian plane.
- A relation is any set of ordered pairs or previously stipulated correspondences between the members of two groups.
- A function is what gives value to a dependent variable for each value of an independent variable in the domain.