# What is lineal funtion?

## What Does lineal funtion Mean

The notion of function has various uses. On this occasion, we are going to focus on the mathematical function : the relationship established between two sets, through which each element of the first set is assigned only one element of the second set, or none at all.

With this clear, we can move on to the idea of a linear function . This is how the mathematical function composed of variables of the first degree is called . It should be noted that a variable is a quantity that, within a certain set, can take on any of the possible values.
A linear function is made up of variables of the first degree.
Characteristics of the linear function
Linear functions are represented by a straight line on the Cartesian plane . It is important to bear in mind that what functions do, in short, is to express a relationship between variables , being able to develop mathematical models that represent this link.

The starting set or initial set is called the domain , while the arrival set or final set is called the codomain . The independent variables are part of the domain ; the dependent variables , of the codomain. When equal changes of an independent variable correspond to equal variations of the dependent variable, we speak of a linear function.
An example
Y = X + 2 is an example of a linear function. Suppose that in the domain we have the values 2 , 5 and 7 . If the function indicates that Y is equal to X + 2 , in the codomain we will find the values 4 , 7 and 9 :
X + 2 = Y

2 + 2 = 4

5 + 2 = 7

7 + 2 = 9
By taking this linear function to a graph in Cartesian coordinates, we will find an increasing straight line : as the values ​​of X increase , the values ​​of Y increase proportionally .
Linear functions, equations, and other concepts often cause difficulties in math classes.
The linear function in geometry and algebra
The concept of a linear function is found in the realm of analytic geometry and in elementary algebra . The first is a branch of mathematics that focuses on the study of figures and their various properties, such as their areas, inclination angles, distances, intersections, volumes, and points of division, among many other characteristics. In short, we can say that it is a very deep vision of geometric figures to know all their data in detail.

On the other hand we have elementary algebra, where those fundamental concepts of algebra are found, the branch of mathematics that focuses on abstract structures and the combination of their elements according to certain rules. For arithmetic, only elementary operations between numbers take place, such as addition, subtraction, multiplication and division; algebra adds the symbols that denote numbers, the so-called variables , and in this way opens the doors to endless possibilities.
The linear function is itself a polynomial function , a relation that assigns a unique value to each instance of the variable and that is made up of a polynomial, an addition or subtraction of a finite number of terms. An example of a polynomial function is f (x) = ax + b , where ax and b are the terms of the polynomial .
As mentioned in a previous paragraph, the linear function always gives straight lines on the Cartesian axes; more precisely, the lines are oblique, and this is the characteristic of first-degree polynomial functions. We have three more degrees: 0 , where the constant function is located , which always produces lines parallel or horizontal to the x-axis; the two , with the quadratic function , which generates the graph it parabolas ; the 3 , which belongs to cubic function , which is plotted in the form of cubic curves.
Retomando la ecuación de función lineal f(x) = ax + b, podemos decir que a y b son constantes reales y x, una variable real. La constante a sirve para determinar la inclinación que tendrá la recta al ser graficada (su pendiente), mientras que b indica el punto en el cual se cortan la recta y el eje y.

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