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A function [10] is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x 2. The output of a function f corresponding to an input x is denoted by f(x) (read "f of x").
In 2005, Emmanuel Schanzer wrote the first version of the Bootstrap curriculum, adapting many of the ideas from the celebrated Program by Design curriculum for use in the context of an 8th grade math class, and inventing a number of teaching techniques (most notably the “Circles of Evaluation”).
An operation can take zero or more input values (also called "operands" or "arguments") to a well-defined output value. The number of operands is the arity of the operation. The most commonly studied operations are binary operations (i.e., operations of arity 2), such as addition and multiplication , and unary operations (i.e., operations of ...
Schematic depiction of a function described metaphorically as a "machine" or "black box" that for each input yields a corresponding output The red curve is the graph of a function, because any vertical line has exactly one crossing point with the curve. A function f from a set X to a set Y is an assignment of one element of Y to each element of X.
Maple has a Math Equation Editor, [33] but does not have a special name for this input method. Texas Instruments calls it MathPrint, [ 34 ] incorporating it in its high-end calculators, such as the TI-Nspire series , and in 2011 added the feature to its TI-84 series with the 2.55 OS update.
For example, (2 + 3) × 4 = 20 forces addition to precede multiplication, while (3 + 5) 2 = 64 forces addition to precede exponentiation. If multiple pairs of parentheses are required in a mathematical expression (such as in the case of nested parentheses), the parentheses may be replaced by other types of brackets to avoid confusion, as in [2 ...