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

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