Domain & Range

Compute the domain of a function:

domain of f(x) = x/(x^2-1)

Compute the range of a function:

range of e^(-x^2)

Compute domain and range of a function of several variables:

domain and range of z = x^2 + y^2

Injectivity & Surjectivity

Determine whether a given function is injective:

is y=x^3+x a one-to-one function?

Determine whether a given function is surjective:

is x^2-x surjective?

Continuity

Determine whether a function is continuous:

is sin(x-1.1)/(x-1.1)+heaviside(x) continuous

Locate discontinuities of a function:

discontinuities (x^3+8)/(x^3+3x^2-4x-12)

Periodic Functions

Compute the period of a periodic function:

period y=sin(x)*cos(3x)

Find periods of a function of several variables:

period sin(x + y^2 - 3z)

Even & Odd Functions

Determine whether a function is even or odd:

what is the parity of sin(x)

is sin(x+pi/4)+cos(x+pi/4) an even function?

is f(x,y,z)=sin(xyz) an odd function?

Special Functions

Compute properties of a special function:

zeta(x)

Numerically evaluate a special function:

sn(2.1, 0.5)

Do computations with special functions:

d/dx Si(x)^2

Number Theoretic Functions

Get information about a number theoretic function:

Euler phi

Do computations with number theoretic functions:

phi(110)

Representation Formulas

Find representations of a function of a given type:

gamma(x) integral representation

Si(x) limit rep