# Library of Functions

**f(x) = x^2**

- Domain: all reals
- Range: from 0 to infinity
- Zeros: x=0
- Symmetry: y-axis, even
- Periodic: no
- One-to-one: no

*f(x) = x^3*

- Domain: all reals
- Range: all reals
- Zeros: x=0
- Symmetry: origin, odd
- Periodic: no
- One-to-one: yes

*f(x) = |x|*

- Domain: all reals
- Range: from 0 to infinity
- Zeros: x=0
- Symmetry: y-axis, even
- Periodic: no
- One-to-one: no

**f(x) = sin x**

- Domain: all reals
- Range: from -1 to 1
- Zeros: integral multiples of pi
- Symmetry: origin, odd
- Periodic: yes, 2pi
- One-to-one: no

*f(x) = cos x*

- Domain: all reals
- Range: from -1 to 1
- Zeros: odd multiples of pi/2
- Symmetry: y-axis, even
- Periodic: yes, 2pi
- One-to-one: no

**f(x) = tan x**

- Domain: all reals expect odd multiples of pi/2
- Range: all reals
- Zeros: integral multiples of pi
- Symmetry: origin, odd
- Periodic: yes, pi
- One-to-one: no

**f(x) = sec x**

- Domai
*n: all reals except odd multiples of pi/2* - Range: all reals
- Zeros: none
- Symmetry: y-axis, even
- Periodic: yes, 2pi
- One-to-one: no

*f(x) = 2^x*

- Domain: all reals
- Range: from 0 to infinity, but not including 0
- Zeros: none
- Symmetry: none
- Periodic: no
- One-to-one: yes

*f(x) = log(base2)x*

- Domain: from 0 to infinity, but not including 0
- Range: all reals
- Zeros: x=1
- Symmetry: none
- Periodic: no
- One-to-one: yes

*f(x) = 1/x*

- Domain: everything except 0
- Range: everything except0
- Zeros: none
- Symmetry: origin, odd
- Periodic: no
- One-to-one: yes

**f(x) = x^(1/2)**

- Domain: from 0 to infinity, including 0
- Range: from 0 to infinity, including 0
- Zeros: x=0
- Symmetry: none
- Periodic: no
- One-to-one: yes

**f(x) = (a^2 - x^2)^(1/2)**

- Domain: from -a to a, including -a and a
- Range: form 0 to a, including 0 and a
- Zeros: x=-a,a
- Symmetry: y-axis, even
- Periodic: no
- One-to-one: no