write function of functional key from f1 to f 12?

A functional key is a unique identifier that maps a specific input from one function to a corresponding output in another function. In this case, the functional key would map inputs from function f1 to outputs in functions f2 through f12.

The function of the functional key would be to establish a relationship between the inputs and outputs of the different functions, allowing for easy and efficient communication between them. This would enable the functions to work together seamlessly and efficiently, ensuring that the desired results are achieved.

Overall, the function of the functional key from f1 to f12 would be to facilitate the flow of information and data between the functions, ultimately leading to the successful execution of a larger, more complex task or process.

Function Description

f1(x) = x + 1
- Adds 1 to the input value x.
- Linear function with a slope of 1 and a y-intercept of 1.

f2(x) = x^2
- Squares the input value x.
- Parabolic function with a vertex at (0, 0).

f3(x) = |x|
- Returns the absolute value of the input value x.
- Piecewise linear function with a slope of 1 for x >= 0 and a slope of -1 for x < 0.

f4(x) = sqrt(x)
- Returns the square root of the input value x.
- Function is defined only for non-negative values of x.

f5(x) = e^x
- Returns the exponential of the input value x.
- Function is increasing and concave up for all values of x.

f6(x) = ln(x)
- Returns the natural logarithm of the input value x.
- Function is increasing and concave down for x > 0.

f7(x) = sin(x)
- Returns the sine of the input value x.
- Periodic function with a period of 2π.

f8(x) = cos(x)
- Returns the cosine of the input value x.
- Periodic function with a period of 2π.

f9(x) = tan(x)
- Returns the tangent of the input value x.
- Periodic function with a period of π.

f10(x) = 1/x
- Returns the reciprocal of the input value x.
- Function is defined for all non-zero values of x.

f11(x) = floor(x)
- Returns the greatest integer that is less than or equal to the input value x.
- Non-continuous, step function.

f12(x) = ceil(x)
- Returns the least integer that is greater than or equal to the input value x.
- Non-continuous, step function.