| Algebraic Functions
| Function |
Domain |
Range |
| f(x) = x |
(-∞ , + ∞) |
(-∞ , + ∞) |
|
f(x) = x 2
|
(-∞ , + ∞) |
[0 , + ∞) |
|
f(x) = x3
|
(-∞ , + ∞) |
(-∞ , + ∞) |
|
f(x) = xn , n even
|
(-∞ , + ∞) |
[0 , + ∞) |
|
f(x) = xn , n odd
|
(-∞ , + ∞) |
(-∞ , + ∞) |
| f(x) = | x | |
(-∞ , + ∞) |
[0 , + ∞) |
| f(x) = Square root ( x ) |
[0 , + ∞) |
[0 , + ∞) |
| f(x) = Cube root ( x ) |
(-∞ , + ∞) |
(-∞ , + ∞) |
Trigonometric Functions
| Function |
Domain |
Range |
| f(x) = sin ( x ) |
(-∞ , + ∞) |
[-1 , 1] |
| f(x) = cos ( x ) |
(-∞ , + ∞) |
[-1 , 1] |
| f(x) = tan ( x ) |
All real numbers except π/2 + n*π |
(-in , + ∞) |
| f(x) = sec ( x ) |
All real numbers except π/2 + n*π |
(-∞ , -1] U [1 , + ∞) |
| f(x) = csc ( x ) |
All real numbers except n*π |
(-∞ , -1] U [1 , + ∞) |
| f(x) = cot ( x ) |
All real numbers except n*π |
(-∞ , + ∞) |
Inverse Trigonometric Functions
| Function |
Domain |
Range |
|
f(x) = sin-1( x )
|
[-1 , 1] |
[-π/2 , π/2] |
|
f(x) = cos-1( x )
|
[-1 , 1] |
[0 , π] |
|
f(x) = tan-1( x )
|
(-∞ , + ∞) |
(-π/2 , + π/2) |
|
f(x) = sec-1( x )
|
(-∞ , -1] U [1 , + ∞) |
[0 , π/2) U [π , 3 π/2) |
|
f(x) = csc-1( x )
|
(-∞ , -1] U [1 , + ∞) |
(-π , -π/2] U (0 , π/2] |
|
f(x) = cot-1( x )
|
(-∞ , + ∞) |
(0 , π) |
Logarithmic and Exponential Functions
| Function |
Domain |
Range |
|
f(x) = a x
|
(-∞ , + ∞) |
(0 , +∞) |
|
f(x) = Log a ( x )
|
(0 , + ∞) |
(-∞ , + ∞) |
|
f(x) = a x + k , k constant
|
(-∞ , + ∞) |
(k , + ∞) |
|
f(x) = Log a ( x - k) , k constant
|
(k , + ∞) |
(-∞ , + ∞) |
Hyperbolic Functions
| Function |
Domain |
Range |
|
sinh(x) = (e x - e -x) / 2
|
(-∞ , + ∞) |
(-∞ , + ∞) |
|
cosh(x) = (e x + e -x) / 2
|
(-∞ , + ∞) |
[1 , + ∞) |
|
tanh(x) = (e x - e -x) / (e x + e -x)
|
(-∞ , + ∞) |
(-1 , + 1) |
|
coth(x) = (e x + e -x) / (e x - e -x)
|
(-∞ , 0) U (0 , + ∞) |
(-∞ , - 1) U (1 , +∞) |
|
sech(x) = 2 / (e x + e -x)
|
(-∞ , + ∞) |
(0 , 1) |
|
sech(x) = 2 / (e x - e -x)
|
(-∞ , 0) U (0 , +∞) |
(-∞ , 0) U (0 , +∞) |
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