Piecewisedefined function
Examples of piecewises
How to set conditions?
Here are some examples of how to set conditions:

x≠0

x is not zero

x > pi

x greater than Pi number

pi/2 <= x <= pi/2

x less than or equal to Pi number in half, but not strictly greater than Pi in half

true

means "otherwise"
What the calculator can do?
On this page you can get various actions with a piecewisedefined function, as well as for most services  get the detailed solution.
 Derivative of a piecewise
 Plot a graph
 Study the function
 Defined integral
 Indefined integral of similar functions
 Limit of piecewises
 Fourier series (In common there are piecewises for calculating a series in the examples)
 Taylor series
First, set the function:
 Piecewisedefined
 Piecewisecontinuous
The above examples also contain:

the modulus or absolute value: absolute(x) or x

square roots sqrt(x),
cubic roots cbrt(x)

trigonometric functions:
sinus sin(x), cosine cos(x), tangent tan(x), cotangent ctan(x)

exponential functions and exponents exp(x)

inverse trigonometric functions:
arcsine asin(x), arccosine acos(x), arctangent atan(x),
arccotangent acot(x)

natural logarithms ln(x),
decimal logarithms log(x)

hyperbolic functions:
hyperbolic sine sh(x), hyperbolic cosine ch(x),
hyperbolic tangent and cotangent tanh(x), ctanh(x)

inverse hyperbolic functions:
hyperbolic arcsine asinh(x), hyperbolic arccosinus acosh(x),
hyperbolic arctangent atanh(x), hyperbolic arccotangent acoth(x)

other trigonometry and hyperbolic functions:
secant sec(x), cosecant csc(x), arcsecant asec(x),
arccosecant acsc(x), hyperbolic secant sech(x),
hyperbolic cosecant csch(x), hyperbolic arcsecant asech(x),
hyperbolic arccosecant acsch(x)

rounding functions:
round down floor(x), round up ceiling(x)

the sign of a number:
sign(x)

for probability theory:
the error function erf(x) (integral of probability),
Laplace function laplace(x)

Factorial of x:
x! or factorial(x)

Gamma function gamma(x)

Lambert's function LambertW(x)
The insertion rules
The following operations can be performed
 2*x
  multiplication
 3/x
  division
 x^2
  squaring
 x^3
  cubing
 x^5
  raising to the power
 x + 7
  addition
 x  6
  subtraction
 Real numbers
 insert as 7.5, no 7,5
Constants
 pi
  number Pi
 e
  the base of natural logarithm
 i
  complex number
 oo
  symbol of infinity