Library of Functions

Charles Landry

y=x^2

  1. Domain- all reals
  2. Range- [0,∞)
  3. Zeros- x=0
  4. Symmetry- y-axis
  5. Even/Odd Function- even
  6. Is the function periodic?- no
  7. Is the function one-to-one?- no


y=x^3

  1. Domain- all reals
  2. Range- all reals
  3. Zeros- x=0
  4. Symmetry- origin
  5. Even/Odd Function- odd
  6. Is the function periodic?- no
  7. Is the function one-to-one?- yes

y=|x|

  1. Domain- all reals
  2. Range- [0,∞)
  3. Zeros- x=0
  4. Symmetry- y-axis
  5. Even/Odd Function- even
  6. Is the function periodic?- no
  7. Is the function one-to-one?- no

y=sinx

  1. Domain- all reals
  2. Range- [-1,1]
  3. Zeros- multiples of pi
  4. Symmetry- origin
  5. Even/Odd Function- odd
  6. Is the function periodic?- yes(2pi)
  7. Is the function one-to-one?- no

y=cosx

  1. Domain- all reals
  2. Range- [-1,1]
  3. Zeros- odd multiples of pi/2
  4. Symmetry- y-axis
  5. Even/Odd Function- even
  6. Is the function periodic?- yes(2pi)
  7. Is the function one-to-one?- no

Y=tanx

  1. Domain- all reals except pi/2 + kpi, k is an integer.
  2. Range- all reals
  3. Zeros- multiples of pi
  4. Symmetry- origin
  5. Even/Odd Function- odd
  6. Is the function periodic?- yes(pi)
  7. Is the function one-to-one?- no

y=secx

  1. Domain- all reals except pi/2 + kpi, k is an integer
  2. Range- (-inf,-1] and[1,inf)
  3. Zeros- none
  4. Symmetry- y-axis
  5. Even/Odd Function- even
  6. Is the function periodic?- yes(2pi)
  7. Is the function one-to-one?- no

y=2^x

  1. Domain- all reals
  2. Range-(0,∞)
  3. Zeros- none
  4. Symmetry- none
  5. Even/Odd Function- neither
  6. Is the function periodic?- no
  7. Is the function one-to-one?- yes

y=logx

  1. Domain- (0,∞)
  2. Range- all reals
  3. Zeros- x=1
  4. Symmetry- none
  5. Even/Odd Function- neither
  6. Is the function periodic?- no
  7. Is the function one-to-one?- yes

y=1/x

  1. Domain- all reals except x cannot equal 0
  2. Range- all reals except x cannot equal 0
  3. Zeros- none
  4. Symmetry- origin
  5. Even/Odd Function- odd
  6. Is the function periodic?- no
  7. Is the function one-to-one?- yes

y=sqrt(x)

  1. Domain-[0,∞)
  2. Range-[0,∞)
  3. Zeros- x=0
  4. Symmetry- none
  5. Even/Odd Function- neither
  6. Is the function periodic?- no
  7. Is the function one-to-one?- yes

y=sqrt(a^2-x^2)

  1. Domain- [-a,a]
  2. Range- [0,a]
  3. Zeros- x=-a x=a
  4. Symmetry- y-axis
  5. Even/Odd Function- even
  6. Is the function periodic?- no
  7. Is the function one-to-one?- no

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