You can use the Boolean command If in order to create a conditional function.
Note: You can use derivatives and integrals of such functions and intersect conditional functions like “normal” functions.
Examples:
·
f(x) =
If[x < 3, sin(x), x^2] gives you a function that equals sin(x) for
x < 3 and x2 for x ≥ 3.
· a ≟ 3 ˄ b ≥ 0 tests whether “a equals 3 and b is greater than or equal to 0”.
Note: Symbols for conditional statements (e. g., ≟, ˄, ≥) can be found in the list next to the right of the Input Bar.
Derivative[Function]: Returns the derivative of the function.
Derivative[Function, Number n]: Returns the nth derivative of the function.
Note: You can use f'(x) instead of Derivative[f]as well as f''(x) instead of Derivative[f, 2] and so on.
Expand[Function]:
Multiplies out the brackets of the expression.
Example: Expand[(x
+ 3)(x - 4)] gives you f(x)
= x2 - x - 12
UK English: Factorise
Factor[Polynomial]:
Factors the polynomial.
Example: Factor[x^2
+ x - 6] gives you f(x) =
(x-2)(x+3)
Function[Function, Number a, Number b]: Yields a function graph, that is equal to f on the interval [a, b] and not defined outside of [a, b].
Note: This command should be used only in order to display functions in a certain interval.
Example: f(x) = Function[x^2, -1, 1] gives you the graph of function x2 in the interval [-1, 1]. If you then type in g(x) = 2 f(x) you will get the function g(x) = 2 x2, but this function is not restricted to the interval [-1, 1].
Integral[Function]: Yields the indefinite integral for the given function.
Note: Also see command for Definite integral
Polynomial[Function]:
Yields the expanded polynomial function.
Example: Polynomial[(x
- 3)^2] yields x2
- 6x + 9.
Polynomial[List of n points]: Creates the interpolation polynomial of degree n-1 through the given n points.
Simplify[Function]: Simplifies the terms of the given function if possible.
Examples:
· Simplify[x + x + x] gives you a function f(x) = 3x.
· Simplify[sin(x) / cos(x)] gives you a function f(x) = tan(x).
· Simplify[-2 sin(x) cos(x)] gives you a function f(x) = sin(-2 x).
TaylorPolynomial[Function, Number a, Number n]: Creates the power series expansion for the given function about the point x = a to order n.