Types of Functions
If the images of x are obtained by simple substitution.
y = 5x − 2
If the images of x cannot be obtained by simple substitution.
5x − y − 2 = 0
In algebraic functions, the operations to be made with the independent variable are: addition, subtraction, multiplication, division, exponents and roots.
Polynomial functions are the functions that are defined by a polynomial.
y = a0 + a1x + a2x² + a3x³ +··· + anxn
Its domain is .
The criterion is given by a real number.
y = b
The graph is a horizontal line parallel to the x-axis.
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 are functions defined by different criteria, according to the intervals being considered.
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.
The independent variable appears as an exponent, an index of root, logarithmic or trigonometric ratios.
Given a positive real number, a, the function that every real number x which corresponds to the power ax is called an exponential function.
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