TYPES OF FUNCTIONS

TYPES OF FUNCTIONS

1. Classified by

   • Elements
     • One one function
       • Every element of the set A is connected to different elements of the set B.
     • Many to one function
       • More than one element of the set A are connected to the same element in the set B.
     • Into function
       • Some elements of set B doesn´t have a pre-image of set A.
     • Onto function
       • Here every element of set B is related and has a pre-imagen on set A
     • Bijection
       • It is a One one function and a Onto function, every element of set A is connected to different elements of set B

2. Classified by

   • Equation
     • Identify function
       • Has the same domain and range. The identity function equation is f(x) = x, it is a straigth line on a graph
     • Linear function
       • Has the same domain and range. The identify function is also a linear function, the equation is y = mx + c
     • Quadratic function
       • Its a second degree equation, the equation of it is s f(x) = ax2 + bx + c, in a graph it has a parabolic shape
     • Cubic function
       • Its a thrid degree equation, the equation of it is s f(x) = ax3 + bx2 + cx +d, The graph of a cubic function is more curved than the quadratic function
     • Polynomial function
       • Based on the power of the polynomial function, the functions can be classified as a 1st degree, 2nd, etc...

3. Classified by

   • Range
     • Signum function
       • Is used to know the sign of the function and does not give the numeric value or any other values for the range
     • Modulus function
       • The modulus function gives the absolute value of the function, its function is f(x) = |x|, it is represented as a V in a graph and only uses the 1st and 2nd quadrant
     • Rational
       • Fraction with polynomials, but if in the polynomial there are exponents, those need to be positive integers in other way it is not a rational function
     • Even and odd
       • Based on the relationship between the input and the output values of the function, is even when the graph is simetric by the y axis, and is odd when is simetric with the point of origin
     • Periodic function
       • Is a function that repeats its values at regular intervals
     • Inverse function
       • The inverse of a function exists, if it is a bijective functionIf a function f(x) = x2 , then the inverse of the function is f-1 (x) = ? −1 (?) = √? .
     • Greatest Integer Function
       • The greatest integer function graph is like some stairs. The greatest integral function is f(x) = ⌊x⌋ or ?(?) = ⟦?⟧.
     • Composite Function

4. Classified by

   • Domain
     • Algebraic function
       • Are the ones who are defined by algebraic expressions as, polynomial, rationals and radicals
     • Trigonometric function
       • Are sin, cos, tan, cotan, sec and cosec, there are also the inverted trigonometric functions where its range is an angle
     • Logarithmic functions
       • Logarithmic functions have a 'log' in the function, and it has a base, they are derivered from exponential functions, this function can be also described in a exponential way

5. Representation

   • Three ways
     • Graph
     • Venn diagram
     • Roster form
       • Ex, {-8,8}

Images and files in the map