Mathematical functions. Introduction and types

What are mathematical functions

Mathematical functions are fundamental tools in the study of relationships between variables. They are expressions that relate one or more variables and generate a specific output or result. These functions can be represented in various forms, such as algebraic equations, graphs or tables of values.

Main types of mathematical functions

There are many types of mathematical functions, each with distinct characteristics and properties. Some of the main types of mathematical functions are as follows:

Linear functions

Linear functions are those whose graphical representation is a straight line. They have the form f(x) = mx + b, where m is the slope and b is the ordinate to the origin.

Quadratic functions

These are functions of second degree, whose graphical representation is a parabola. They have the form f(x) = ax² + bx + c, where a, b and c are constants.

Exponential functions

They are those in which the independent variable is in the exponent. They have the form f(x) = a^x, where a is a constant and x is the variable.

Logarithmic functions

They are the inverse of the exponential functions. They have the form f(x) = log_ax, where a is a constant and x is the variable.

Trigonometric functions

They include the sine, cosine, tangent functions, among others. These functions are related to the angles of a triangle and have applications in geometry, physics and other disciplines.

Polynomial functions

They are those that are formed by an addition or subtraction of terms of integer powers. They have the form f(x) = a_nxⁿ + a_n-1x^n-1 + … + a₁x + a₀,, where a₀, a₁, …, a_n are constant coefficients.

These are just a few examples of mathematical functions. The choice of the appropriate function depends on the context and the relationship to be modeled. The study and understanding of mathematical functions are fundamental to solve problems and analyze phenomena in various areas of knowledge.