Classification of functions
Algebraic functions
In algebraic functions, the operations to be carried out with the independent variable are: Addition , Subtraction , Multiplication , Division , Empowerment and Radication .
The algebraic functions include:
Explicit functions
If the images of x can be obtained by simple substitution.
f (x) = 5x – 2.
Implicit functions
If the images of x cannot be obtained by simple substitution, it is necessary to carry out operations.
5x – y – 2 = 0.
Polynomial functions
They are the functions that are defined by a polynomial .
f (x) = a 0 + a 1 x + a 2 x² + a 2 x³ + ··· + a n x n
Its domain is R, that is, any real number has an image.
Constant functions
The criterion is given by a real Number .
f (x) = k.
The Graph is a horizontal line parallel to the axis of the Abscissa .
First degree polynomial functions
f (x) = mx + n.
Its Graph is an oblique line, which is defined by two points of the Function .
- Related function.
- Lineal funtion.
- Identity function.
- Quadratic functions.
f (x) = ax² + bx + c.
They are polynomial functions of the second degree, being its graph a Parabola .
Piecewise Functions
They are functions defined by different criteria, according to the intervals considered.
- Functions in absolute value.
- Function integer part of x.
- Mantissa function.
- Sign function.
Rational functions
The criterion is given by a quotient between polynomials:
f (x) = a 0 + a 1 x + a 2 x 2 + — + a n x n .
b 0 + b 1 x + b 2 x 2 + — + b m x m
The domain is made up of all real numbers except the values of x that cancel the denominator.
Radical functions
The criterion is given by the variable x under the radical sign.
The domain of an irrational function with an odd index is R.
The domain of an irrational function of even index is made up of all the values that make the radicand greater than or equal to zero.
Transcendent functions
The independent variable appears as an exponent, or as a root index, or is affected by the logarithm sign or any of the signs that trigonometry uses .
Exponential function
f (x) = a x
Let be a positive real number. The function that makes each power number x correspond to the power ax is called the exponential function of base a and the exponent x.
Logarithmic functions
The logarithmic function based on is the inverse function of the exponential based on.
f (x) = log a x
a> 0, a ≠ 1.
Trigonometric functions
Sine function
f (x) = sin x.
Cosine function
f (x) = cos x.
Tangent function
f (x) = tg x.
Cosecant function
f (x) = cosec x.
Drying function
f (x) = sec x.
Cotangent function
f (x) = cotg x.
