# 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

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

Page last updated 3 March 2002.

# Brian’s Casio Calculator Corner

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Introduction

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Introduction

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Grouping

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String

Side Effect

Functions

Control Flow I

Control Flow II

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A First Program

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