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 for functions 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 integral representations for a function

gamma(x) integral representation

sqrt(x) continued fraction