Calculator Programming Tutorial

Programming Building Blocks I

Expressions

Functions

Mathematically, a function is a mapping from a domain set into a range set, such that any point in the domain set is mapped into a single point in the range set. Thus, for example, we can define a function f mapping the set of people into the set of colors, such that f(x) is the favorite color of the person x. Some of the points of this function might be:

x	f(x)
Brian	Blue
Lisette	Blue
Grandmom	Red
Hikage	Black
Cindy	Purple
Mad Pumpkin	Blue

It is not necessary that the values of the function f(x) be distinct for distinct values of x: note how many people like blue. If all function values are distinct, though, the function is called a bijection, or a one-to-one function. For example, the positive square root function maps any non-negative number to another non-negative number, and does so uniquely: every non-negative number is the square root of exactly one other non-negative number.

In computers, a function is a subprogram that returns a value that can be used in an expression. For example, the square root operation is a function. The square root of a value x is expressed in JavaScript as Math.sqrt(x), in VBA as Sqr(x), and in the calculator as √ x.

User written functions will be covered in greater detail in the Subprograms section. However, the calculator, JavaScript, and Visual Basic for Applications all provide a set of “built-in” functions. Some of the more popular functions are given in the following table.

Name	Mathematics	JavaScript	VBA	Calculator
Absolute value	\|x\|	Math.abs (x)	Abs (x)	Abs x
Square root	√ x	Math.sqrt (x)	Sqr (x)	√ x
Natural logarithm	ln x	Math.log (x)	Log (x)	Ln x
Common logarithm	log x	(none)	(none)	Log x
Sine, cosine, tangent	sin x, cos x, tan x	Math.sin (x), Math.cos (x), Math.tan (x)	Sin (x), Cos (x), Tan (x)	sin x, cos x, tan x
Arc sine, arc cosine, arc tangent	sin^-1 x, cos^-1 x, tan^-1 x	Math.asin (x), Math.acos (x), Math.atan (x)	(none), (none), Atn (x)	sin^-1 x, cos^�1 x, tan^�1 x