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