FUNCTIONS

FUNCTIONS

1. Is defined as the depency between the elements of two given sets.

   • between them is an association (f)
     • that
       • assigns a single element of b to each element of A
         • these functions are divided into
           • LINEAR FUNCTION
             • is a polynomial function of the first degree
               • means that it is of the form
                 • f(x) = m * x + n
                   • m = the slope of the function
                   • m ≠ 0
                   • n = the ordinate (at the origin) of the function
               • the graph of this function is always a line
           • QUADRATIC FUNCTION
             • is a second degree polynomial function
               • means that it is of the form
                 • f(x) = ax^2 + bx + c
                   • a ≠ 0
               • The graph of a quadratic function is always a parabola
           • QUBIC FUNCTION
             • is polynomial function of degree 3
               • it´s general form is
                 • f(x) = ax^3 + bx^2 + cx + d
               • The graph of a quadratic function is
           • EXPONENTIAL FUNCTION
             • is the one in which the independent variable x appears in the exponent
               • and
                 • has a constant a as its base
                   • the graphic of this function is
               • its general form is
                 • f(x) = a^x
                   • being A a real positive, a>0 a ≠ 1.
           • CONSTANT FUNCTION
             • is a polynomial function of degree 0
               • its general form is
                 • f(x) = k
               • the graph of this function is a horizontal line
           • EULER FUNCTION
             • is an important function in number theory
               • If n is a positive integer
                 • φ (n) is defined as the number of
                   • positive integers less than or equal to n and coprime with n.
               • the graph of this function is
             • φ = 2.7
           • LOGARITHM FUNCTION
             • whose base is 10
               • therefore
                 • it is the exponent to which we must raise 10 (exponentiation) to obtain said number
             • the graphic of this function is
           • ROOT FUNCTION
             • are those in which the variable is under the radical sign
               • the graph of this function is
             • are positive functions
               • since in the definition
                 • only the positive root of the radicand is considered
             • is divided into two types
               • odd index
               • even index
           • NATURAL LOGARITHM FUNCTION
             • this one is defined for positive real values
               • the graphic of this function is
             • the number for which this function is equal to 1 turns out to be the number e
               • therefore
                 • ln is the logarithm with base e
           • POLYNOMIAL FUNCTION
             • is a function whose expression is a polynomial such as
               • • a n ≠ 0
               • They are continuous functions whose domain is the set of real numbers.
               • the graph of this function is
           • INJECTIVE FUNCTION
             • is if each element of the final set Y has a single element of the initial set X to which it corresponds
               • that is
                 • there cannot be more than one value of X that has the same image Y
             • the graphic of this function is
           • SURJECTIVE FUNCTION
             • is a function such that
               • all elements of the final set Y have at least one element of the initial set X
                 • to which it corresponds
             • the graphic of this function is

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