Functions

# Mathematical functions. Function Builder

## Do you know what a mathematical function is, what it is used for and what types there are?

Online mathematical function simulations allow us to visualize what a mathematical function is and to build some examples.

Online mathematical function simulations allow us to visualize what a mathematical function is and to build some examples.

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.

There are many types of mathematical functions, each with distinct characteristics and properties. Some common examples are:

**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) = ax^{2} + 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_{a}x, 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_{n}x^{n} + a_{n-1}x^{n-1} + … + a_{1}x + a_{0},, where a_{0}, a_{1}, …, 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.

**Below are several simulations and other educational resources, which can also serve as very illustrative examples. In addition, a selection of books and courses is included to help you broaden your knowledge of this subject.**

- Intro
- Builder

## Introduction to mathematical functions

Play with functions while reflecting on the History of Art. Look for patterns, then apply what you've learned on the Mystery!!! screen.

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## Function builder

Play with functions while reflecting on Art History. Explore geometric transformations and change your thinking about linear functions, then have fun discovering the mystery functions!

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###### Mathematics

MathTrackX: Polynomials, Functions and Graphs

###### Cálculus

Multivariable Calculus 2: Integrals