Math

# 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.