FUNCTION

FUNCTION

1. A function ( f ) is a given relationship between X ( domain ) and another set of assembly elements Y ( codomain ) so that each element x of the domain has a single element f ( x ) forming the codomain the range

   • Algebraic Functions
     • Explicit Functions
       • If you can get the images of x by simple substitution
         • EXAMPLE: f(x)=5x-2
     • Implict Functions
       • If you can not get images of x by simple remplecet it is necesary to carry out operations
         • EXAMPLE: 5x-y-2=0
     • POLYNOMIAL FUNCTIONS
       • Constant function
         • f(x)=k
           • the graph is a horizontal line parallel to horizontal axi
       • Linear Function
         • f(x)=mx+n
           • domain (-∞,∞) range(-∞,∞) decreasing m< 0 growing m> 0
       • Quadratic function
         • f(x)=x^n
           • the are polynomial functions is second grande and its graph a parabola
     • RATIONAL FUNCTION
       • A rational function f is said if you can be viewed as the ratio of polynomials, ie the criterions is given by a rato of polynomials
         • f(x)=P/Q Q ≠0
     • RADICAL FUNCTION
       • Are functions that have the independent variable x nder the radical
     • APPLICATION
       • The rate of taxis in a city provides charged for each kilometer travel the same amount over the checkered flag , that is, at the time that the driver is hired a fixed rate , independent of the kilometers to cross amount is added . a day, a person hired a taxi , walked 3 km and took 15UM . Another day took another taxi that he took a career 25um 8km . a) Justify that there is a linear relationship between x, number of kilometers and T, charging rate . b ) Express the rate as a function of time
         • T = 2x + 9 T(x) 2x + 9 Dom T=[0, ∞)
   • TRANSCENDENTAL FUNCTION
     • EXPONENTIAL FUNCTION
       • f(x)=a^x
         • Be a positive real number the function that each real number x makes it match the power exponential ax is called base ay exponent
     • LOGARITHMIC FUNCTION
       • f(X)=log X
         • domain (0, ∞) range (- ∞, ∞)R it is the inverse of the exponencial function f(x)=a^x
     • TRIGONOMETRIC FUNCTIONS
       • SINE
         • f(x)= sinx
       • COSINE
         • f(x)= cosx
       • TANGENT
         • f(x)=tgx
       • SECANT
         • f(z)=secx
       • COSECANT
         • f(x)=cscx
       • COTANGENT
         • f(x)= cotgx
     • APPLICATION
       • The law of cooling bodies states that the cooling Newton a body is proportional at each instant , the difference room temperature. The law says that if T0 is the initial temperature at which we introduce a body in an environment with a temperature of Ta degrees , after a t time the body temperature is T ( t) = Ta + (T0 - Ta ) and -α t where α is a constant, called the constant cooling , and is each particular body.
   • PRECEWISE FUNCTIONS
     • The are functions defined by different criteria, the inteval are consideres
     • Integer part of x functions
       • It is a fectuare that makes each real number corresponds the nearest whole number
     • Mantisa function
       • Function that maps each number to the same number unless your entiere part
     • function sign
     • absolute value function
     • APPLICATION
       • A disease spreads over time at a rate of x² + 2x if x -1, people a day. If the disease begins when presented the following three symptoms: chills, fever and tinnitus in 3 patients , find the parts function and describe through a graphical
         • is increasing, decreasing and constant due to variation of symptoms , therefore the speed of propagation

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