MATHEMATICAL FUNCTIONS

MATHEMATICAL FUNCTIONS

1. ALGEBRAIC FUNCTIONS

   • Algebraic functions call those that can be expressed in terms of a finite number of sums, differences, products, quotients and roots.
     • They can be represent as: f(x)=√x2+1
   • POLYNOMIAL FUNCTION
     • A f is a polynomial function if f (x) = anxn + an-1xn-1 + ... + a1x + a0, where a0, a1, ..., an are real numbers and the exponents are positive integers
     • CONSTANT FUNCTIONS
       • A function of the form f (x) = b, where b is a constant. For example, f (x) = 3 (corresponding to the value of y) where the domain is the set of real numbers and the route is {3}, then y = 3.
     • LINEAR FUNCTION
       • A function of the form f (x) = mx + b. where m represents the slope and b represents the intercept. The graphical representation of a linear function is a line. Linear functions are polynomial functions. For example: f (x) = 2x - 1 is a linear function with slope m = 2 and y-intercept (0, -1).
     • QUADRATIC FUNCTION
       • f(x) = ax² + bx + c
   • RATIONAL FUNCTION
     • A rational function f is a ratio of two polynomials: f(x)=P(x)/Q(x), where P and Q are polynomials. The domain consists of all values of x such that Q (x) ≠ 0.
       • A simple example of a rational function is the function f (x) = 1 / x, whose domain is {x ≠ 0}; this is the reciprocal function
   • RADICAL FUNCTIONS
     • The function f(x)=x1/n=n√x It is a root function. For n = 2 is the square root function f (x) = √ x, whose domain is [0, ∞} and whose graph is the upper half of the parabola x = y2. For others even values of n, the graph y=n√x It is similar to that of y = √x. For n = 3 we have the cube root function f(x)=3√x whose domain is R.
   • piecewise functions

2. a function (f) it is a relation between a given set X (called domain) and another set of elements Y (named range) so that each element x of the domain has a single element f (x) range.

3. TRANSCENDENTAL FUNCTIONS

   • In transcendental functions independent variable appears as exponent, or as an index of the root or the logarithm is affected either sign or signs used trigonometry.
     • EXPONENTIAL FUNCTION
       • Be a positive real number. The function that each real number x makes it match the power exponential function ax is called base ay exponent x.
     • LOGARITHMIC FUNCTION
       • The logarithmic based function is the inverse of the exponential function based on.
     • TRIGINOMETRIC FUNCTION
       • The trigonometric functions associated with each real number x, the value of the trigonometric ratio of the angle whose radian measure is x.
         • SINE FUNCTION
           • f(x) = sen x

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