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.
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 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.
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
