# Types of Functions

#### Explicit Functions

If the images of x are obtained by simple substitution.

y = 5x − 2

#### Implicit Functions

If the images of x cannot be obtained by simple substitution.

5x − y − 2 = 0

## Algebraic Functions

In algebraic functions, the operations to be made with the independent variable are: addition, subtraction, multiplication, division, exponents and roots.

### Polynomial Functions

**Polynomial functions are the functions that are defined by a polynomial.**

y = a_{0 } + a_{1}x + a_{2}x² + a_{3}x³ +··· + a_{n}x^{n }

Its domain is .

#### Constant Functions

**The criterion is given by a real number.**

**y = b **

The **graph** is a **horizontal line** parallel to the x-axis.

#### Linear Function

**y = mx + b**

Its **graph** is an **oblique straight line**, which is defined by two points of the function.

#### Quadratic Functions

**y = ax² + bx +c **

Its **graph** is a **parabola**.

#### Piecewise Functions

Piecewise functions are functions defined by different criteria, according to the intervals being considered.

### Rational Functions

The criterion is given by a quotient between polynomials:

The domain is equal to , but does not include the values of x that would annul the denominator.

### Radical Functions

The criterion is given by the variable x under the radical sign.

The domain of a radical function of odd index is .

The domain of a radical function of even index is equal to all values that make the radical greater than or equal to zero.

## Transcendental Functions

The independent variable appears as an exponent, an index of root, logarithmic or trigonometric ratios.

### Exponential Functions

Given a positive real number, **a**, the function that every real number x which corresponds to the power **a ^{x}** is called an exponential function.

### Logarithmic Functions

The** logarithmic function** in base **a** is the **inverse function** of the **exponential function** in base **a**.

### Trigonometric Functions

#### Sine Function

**y = sin x**

#### Cosine Function

**y = cos x**

#### Tangent Function

**y = tan x**

#### Cosecant Function

**y = csc x**

#### Secant Function

**y = sec x**

#### Cotangent Function

**y = cot x**