Function Commands

Conditional Functions

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

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

Expand[Function]: Multiplies out the brackets of the expression.     
Example: Expand[(x + 3)(x - 4)] gives you f(x) = x2 - x - 12

Factor

UK English: Factorise

 

Factor[Polynomial]: Factors the polynomial. 
Example: Factor[x^2 + x - 6] gives you f(x) = (x-2)(x+3)

Function

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

Integral[Function]: Yields the indefinite integral for the given function.

 

Note: Also see command for Definite integral

Polynomial

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

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

TaylorPolynomial[Function, Number a, Number n]: Creates the power series expansion for the given function about the point x = a to order n.


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