The concept of function is important when it is associated with certain subjects, in which the representations that the word has can serve a common objective. We speak of a function, in its simplest sense, when we proceed to the elaboration of a system of actions that lead to the completion of a plan. This can refer to the reason for what something is used, such as the telephone, which is used to communicate, so the objective of it is to transmit information.
What is function
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In general terms, a function is that objective or purpose that an individual, an object, a process or a situation has. In other words, it is the “what for” of an element, what it is made for or what it is found for in a certain place. As a verb "to function ", it refers to the way in which an object, device, system or individual interacts or carries out its task or process, that is, how it works. It is a concept that tangibly encompasses everything related to a process and an objective, relating all the actions of its kind that may be needed.
This term is also used for everything that is done focused on a specific purpose, hence the term to perform something "based on", referring to all that action that is carried out to achieve a goal. It is an ideal tool for solving problems, it supposes a more determined concept to an action to be carried out.
In the same way, it can be a type of exhibition or show. For example, when we go to see a movie, it is to see a cinema function, in which an establishment develops its service and people enjoy it. In the same way the term can be associated with a public or private event but in which some art is exhibited.
Colloquially, this word can be used to refer to some type of altercation or discussion that occurs between two or more people and that has gotten out of proportion causing a scandal.
Its etymology comes from the Latin "functio" which means "execution or exercise of some faculty or the fulfillment of a duty". In our language, the term can be conceived as: the capacity of a living being, the task proper to the activity, a massive theatrical act or a relationship between two or more elements.
What is a mathematical function
In the mathematical field it is a didactic and practical tool with which situations or problems to be solved are defined. In mathematics represents is the correspondence between two sets, so that an element of the first set corresponds to another unique element of the second set, which will become a dependent variable.
This process must comply with a basic scheme, and it is in which there is a relationship between two forms, objects or two representations with an operator between them, and each element of each part must maintain a relationship with everything within the function.
These are a graphical representation of the two sets. This graph will define some abstract result for any other area, but within a context and mathematical logic, it will make sense. The functions in this sense can represent the path of a particle.
Types of mathematical function
According to the correspondence of the first set with the second, there will be different types, which can be:
Mathematical function
It is the dependency relation of an independent variable (X), also called " domain "; and a dependent variable (Y), also called " codomain ", which together will form what is called "tour", "scope" or "range".
There are three ways to express a mathematical function, which are in graphical form where a system of four quadrants determined by the X (horizontal) and Y (vertical) axes called the Cartesian plane is used; in an algebraic expression; and / or in a table of values.
Usually for each value of X, only one value of the dependent Y will correspond, unless it is about other types of functions that will allow the variable Y to have more than one value of the variable X. This means, in functions that the variable Y can be related to more than one value of the variable X. These are known as surjectives.
Rational function
Rational numbers are the quotient of two whole numbers, their denominator being different from zero. The rational function is one that is represented by a hyperbola (open curve with two opposite branches) and is characterized by presenting asymptotes (a line to which the function continuously approaches infinity without actually coinciding). Its center will be the intersection point of the asymptotes.
Algebraically, this type of function is represented as follows:
- Where G and L are polynomials and x is a variable. In this type, the domain will be all those values of x of the line, so that the denominator is not annulled, so all the numbers will be real, except when x = 0, being at this point where it will have the vertical asymptote.
- According to the sign of G, if it is greater than 0, the hyperbola is in the first and third quadrants; and if it is less than 0 it will be found in the second and fourth quadrants, the center of the hyperbola being the coordinate 0, 0 (value for x = 0 x = 0 and y = 0).
Lineal funtion
It is one formed by a first degree polynomial, which is represented by a straight line on the Cartesian axis, which, algebraically symbolized, will look like this: F (x) = mx.
The letter m symbolizes the slope of the line, that is, the inclination of the slope with respect to the abscissa (x) axis. In the case that x has a positive value (greater than 0), then the function will be increasing. Now, if m has a negative value (less than 0), the function will be decreasing.
Trigonometric function
These are those that are associated or related to a trigonometric ratio. These arose when observing a right triangle and observing that the ratios between the lengths of two of its sides are only subject to the value of the angles of the triangle.
To define the functions of the angle alpha of a right triangle, the hypotenuse (side opposite to the right angle, being the largest side), the opposite leg (the side opposite to said angle alpha) and the adjacent leg (the side adjacent to angle alpha).
The six basic trigonometric functions that exist are:
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1. Sine, which is the relationship between the length of the opposite leg with that of the hypotenuse, being:
2. Cosine, is the relationship between the length of the adjacent leg and the hypotenuse, so:
3. Tangent, relationship between the length of the opposite leg and the adjacent leg, where:
4. Cotangent, relationship between the length of the adjacent leg and the opposite leg:
5. Secant, is the relationship between the length of the hypotenuse and the adjacent leg:
6. Cosecant, relationship between the length of the hypotenuse and the opposite leg, being:
Exponential function
It is the one where its independent variable X appears in the exponent, based on its constant a, expressed as follows: f (x) = aˣ
Where a is a positive real number greater than 0 and different from 1. If the constant a is greater than 0 but less than 1, then the function is decreasing; whereas if it is greater than 1, then the function will be increasing. This type is also expressed as exp (x) and is considered as the inverse of the logarithmic function.
The properties of the exponential function are: exp (x + y) = exp (x).exp (y); exp (xy) =; and exp (-x) =.
Quadratic function
Also known as a second degree function, It is one where its exponent will not be greater than 2. Its formula is expressed as follows: f (x) = ax 2 + bx + c
The graphical form in the Cartesian plane of this type of mathematical tool is a parabola, and it will open up or down depending on the sign or value of a: if the constant a is greater than 0, the parabola will open up; and if it is less than 0, it will open down.
This can have one, two or no solution, which will mean one, two or no cut with the abscissa axis (X axis).
Logarithmic function
It is determined by a logarithm (exponent to which the base must be raised to obtain said number). Its algebraic formula is conformed as follows: logb y = x
Where a is a positive real number greater than 0 and different from 1. When a is less than 1 and greater than 0, the logarithmic function will be decreasing; while if it is greater than 1, it will be increasing. The logarithmic function is the inverse of an exponential function. Its domain is made up of positive real numbers and its path is real numbers.
Polynomial function
Also called a polynomial, it is a relationship in which each value of X is assigned a unique value as a result of substituting it in a polynomial associated with the function. It is expressed algebraically in the following way: 4x + 5y + 2xy + 2y +2.
There are different types of polynomial relations according to their polynomial degree, which are:
- Constants, which are those of degree 0, where 0 is the coefficient of x, without depending on the independent variable X: where a is a constant.
- First degree, which comprise a scalar that multiplies the variable X plus a constant, X1 being its greatest exponent, so that it looks like this: where m is the slope and n the ordinate (value from 0 to the cut-off point on the Y axis). According to the value of m and n there are three types of polynomial functions of the first degree: affine (which do not pass through the origin), linear (the ordinate is 0 and m is the slope other than 0) and identity (each element of X is equal to its value in Y).
- Quadratic, grade 2, already explained previously.
- Cubic, which are of degree 3, so its greatest exponent will be X3, like this: where a is different from 0.
Function in calculation
It is a set of elements whose value corresponds to a single value of a second set of elements. Said relationship will be illustrated through a diagram in which the points of intersection of said corresponding values will be indicated, which, in their entirety, will form a graph that will represent a route.
To understand the meaning of function in calculus, the following concepts must be taken into account:
- Domain: They are all the values that the independent variable X can take, in such a way that the dependent variable Y is a real number.
- Range: Also called a contradomain, it is the group of all the values that a function can take and depend on the values of X.
Other types of function
In different contexts, other types of functions can be conceived, among which we can highlight:
Body functions
The human body performs countless tasks or functions, which can be vital and non-vital. The non-vital functions of the human body are those that, although they are important, are not essential to keep the organism alive, such as movement, since a person can remain all his life without walking.
The vital functions are those without which the functioning of the body and, therefore, life in it would not be possible. These, also called vegetative, are:
- Nutrition: This involves the digestive, circulatory, respiratory and excretory systems. For the latter, other functions are involved, such as the function of the liver, sweat glands, lungs, and kidneys.
- Relationship: The endocrine system and the nervous system are involved here. The nervous system, in turn, is divided into the central nervous system (brain and spinal cord) and peripheral nervous system (somatic nervous system: afferent and efferent nerves; and autonomic nervous system: sympathetic and parasympathetic nervous system).
- Reproduction: The male and female reproductive systems are involved. Although this is not vital for a single individual to stay alive, it is vital for the perpetuity of the species.
In the body there are many elements that have a specific mission. The functions of proteins, for example, are structural, enzymatic, hormonal, regulatory, defensive, transport, among others. The function of lipids is similar to that of proteins, since they also fulfill reserve, structural and regulatory functions. The function of the brain is to control the central nervous system, it is responsible for thinking and controlling the body. In a cell, the function of the nucleus is to preserve and control its own genes and activities.
Language functions
When it comes to communicating a message within language, it is done with an intention and an objective, which will depend on which element that intervenes in it will have a greater role. These elements are: sender, receiver, message, channel, context and code. According to this, the purpose of the language is:
- Representative or referential: allows to transmit a message objectively, informing facts or ideas, with the thematic context being the predominant element.
- Expressive: This allows to express feelings, wishes or opinions from a subjective point of view, the issuer being the predominant element.
- Conative or appellate: Its objective is to influence the behavior of the receiver to induce a reaction or to do something. Its predominant element is the receptor.
- Phatic: consists of extending, creating or interrupting communication. Its predominant element is the channel.
- Metalinguistics: its objective is to use language to refer to the same language, its predominant element being the code (language).
- Poetic: It is presented in literary texts, which seeks to alter everyday language with an objective, the expressive form being important. Its predominant element is the message.
Functions in Excel
In the computing context, specifically for applications and work tools such as Excel, it is a predetermined formula that is used to perform calculations through values or arguments that the user provides in a specific order. These allow the user to avoid making such calculations by hand and one by one.
To understand how these formulas work in Excel, it is necessary to define their syntax, which is as follows: the use of the equal sign (=), the function to be performed (if it is addition, subtraction, etc.) and finally the arguments or data that will complete the formula. The latter are supplied by the user, which can be cell ranges, text, values, cell comparisons, among others.
The application has a wide range of tools to facilitate and complement the work of a person, and are grouped into: search and reference, text, logic, date and time, database, mathematics and trigonometric, financial functions, statistics, information, engineering, cube and web.
Public function
This concept is related to the tasks and responsibilities that are assigned to an institution, body, entity, foundation or corporation, which are of public interest and character, to work focusing on the provision of a service of local, regional or national interest.
Usually these bodies belong to the State of a nation, who will be in charge of the exercise of said public activity, also called public administration. Its employees are referred to as civil servants or civil servants.
