Chapter 4 - Functions |
| Functions - Factorial Functions - Contents |
The basic factorial function has the specific form y equals x factorial. The function x factorial is the operation of multiplying the variable x times (x minus one) times (x minus two) times (x minus three) etc. until it reaches the final integer one. In other words, it is the multiplication of all the integers starting at one, the natural numbers, up to the x value. Any non-integer x is rounded down to the integer form. The factorial of zero is one by definition. The factorial function has a limited domain for the x variable which is the set of all real numbers where x is greater than or equal to zero. The range of the factorial function is a specific set of integers greater than zero: 1, 2, 6, 24, 120, 720 . . . It is still an infinite set.
| Functions - Factorial Functions - Examples |
Factorial function form:
y = x!
y equals x
factorial
Two factorial examples:
If y = x!, and x = 3,
then y = 3 x 2 x 1 = 6,If y = x!, and x = 5.7,
then y = 5 x 4 x 3 x 2 x 1 = 120.In both cases the domain is inferred to be x >= 0.
| Functions - Factorial Functions - Mysteries |
Math Mysteries: The factorial function increases even faster than the better known exponential function. As x increases incrementally from one, y is equal to 1, 2, 6, 24, 120, 720, 5040 . . . It increases extraordinarily rapidly. If something is multiplying super fast it should be said that it is increasing factorially instead of exponentially.
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