# Difference Between Function and Formula

To begin with, the term mathematics comes from the Greek -mathema-, which means learning, study and science, this is responsible for the study of topics such as calculation, geometry, among others. This science was born from the need of man to count objects to carry out the trade that, at that time, was known as bartering. From there, the basic operations such as addition, subtraction, multiplication and division arose and, in turn, the first steps were taken towards the study of geometry. Next, notation and writing began, beginning with the use of knots in strings up to the numbers that we currently use.

Thus, within mathematics there are some important concepts such as logic, which is responsible for formal systems such as computations and demonstrations. In addition, there are the mathematical functions, which are responsible for relating their elements to a result, and finally there are the formulas, which are the ones that determine the relationship between quantities and the induction that proves the assertion in natural numbers.

In this sense, in this article we will make a more detailed description of the mathematical functions and formulas, explaining some of their qualities in each concept and then summarizing their differences.

**The functions**

They are mathematical operations that are already predetermined and that are used to perform calculations, whether simple or complex, with the data that is supplied. Also, it is said that it is a norm that applies to two sets in such a way that only one element of the other set corresponds to the first set.

In a function, the elements of a set called the domain are taken and related to the elements of another set called the codomain, where the output is called the image and they are the true values of a function. On the other hand, its usefulness can occur in various situations and is applicable in other sciences. Generally, the letter “f” is used to name a function, but the use of other letters or terms for it is not ruled out.

Finally, we can say that there are different types of functions, among which we can mention the linear function, the constant function, rational function, quadratic function, power function, square root function.

**The formulas**

A formula is a procedure that allows solving or solving a mathematical operation, that is, it is a short statement that facilitates the practical and simple organization of data in a symbolic way.

These are made up of constant symbols, function symbols, and relationship symbols. Thus, within a formula numbers, letters of the Spanish or Greek alphabet can be used to designate constants and variables. Functions, logical symbols, punctuation marks, among others, are also used. It is worth noting that formulas are used in algebra, natural sciences, computer science and social sciences.

Once these mathematical terms have been characterized, the differences between function and formula are described below:

- A function relates inputs to outputs while a formula is made up of constant symbols, function symbols, and relation symbols.
- A function is an application of one set over another while a formula is used to represent a mathematical problem or operation.
- A function is made up of a set (domain), a codomain, and an image, while a formula is made up of constants and variables, as well as function symbols and relationship symbols.