# 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 = a0 + a1x + a2x² + a3x³ +··· + anxn

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.

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.

Floor function.

### 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.

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 ax is called an exponential function.

### Logarithmic Functions

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

y = sin x

y = cos x

y = tan x

y = csc x

y = sec x

y = cot x

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