# Library of Functions

f(x) = x^2

1. Domain: all reals
2. Range: from 0 to infinity
3. Zeros: x=0
4. Symmetry: y-axis, even
5. Periodic: no
6. One-to-one: no

f(x) = x^3

1. Domain: all reals
2. Range: all reals
3. Zeros: x=0
4. Symmetry: origin, odd
5. Periodic: no
6. One-to-one: yes

f(x) = |x|

1. Domain: all reals
2. Range: from 0 to infinity
3. Zeros: x=0
4. Symmetry: y-axis, even
5. Periodic: no
6. One-to-one: no

f(x) = sin x

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

f(x) = cos x

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

f(x) = tan x

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

f(x) = sec x

1. Domain: all reals except odd multiples of pi/2
2. Range: all reals
3. Zeros: none
4. Symmetry: y-axis, even
5. Periodic: yes, 2pi
6. One-to-one: no

f(x) = 2^x

1. Domain:  all reals
2. Range:  from 0 to infinity, but not including 0
3. Zeros:  none
4. Symmetry:  none
5. Periodic:  no
6. One-to-one:  yes

f(x) = log(base2)x

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

f(x) = 1/x

1. Domain:  everything except 0
2. Range:  everything except0
3. Zeros:  none
4. Symmetry:  origin, odd
5. Periodic:  no
6. One-to-one:  yes

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

1. Domain: from 0 to infinity, including 0
2. Range: from 0 to infinity, including 0
3. Zeros: x=0
4. Symmetry: none
5. Periodic: no
6. One-to-one: yes

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

1. Domain: from -a to a, including -a and a
2. Range: form 0 to a, including 0 and a
3. Zeros: x=-a,a
4. Symmetry: y-axis, even
5. Periodic: no
6. One-to-one: no