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# Lesson 11.2: Function Name Abbreviation

## Explanation

Function names are usually mathematical expressions. The rules about mathematical expressions often apply to function names, such as the rules regarding punctuation. Function names often are abbreviated, such as sin for sine. Other rules also apply to function names and are explained in this lesson.

The following is a brief list of some common function names and the abbreviations used for them. The function name is presented first, followed by its abbreviation. When reading through the list, note should be taken of when braille contractions are and are not used.

$\text{logarithm,}\phantom{\rule{.3em}{0ex}}\mathrm{log}$
⠇⠕⠛

$\text{natural logarithm,}\phantom{\rule{.3em}{0ex}}\mathrm{ln}$
⠇⠝

$\text{exponential,}\phantom{\rule{.3em}{0ex}}\mathrm{exp}$
⠑⠭⠏

$\text{limit,}\phantom{\rule{.3em}{0ex}}\mathrm{lim}$
⠇⠊⠍

$\text{sine,}\phantom{\rule{.3em}{0ex}}\mathrm{sin}$
⠎⠊⠝

$\text{hyperbolic sine,}\phantom{\rule{.3em}{0ex}}\mathrm{sinh}$
⠎⠊⠝⠓

$\text{cosine,}\phantom{\rule{.3em}{0ex}}\mathrm{cos}$
⠉⠕⠎

$\text{hyperbolic cosine,}\phantom{\rule{.3em}{0ex}}\mathrm{cosh}$
⠉⠕⠎⠓

$\text{tangent,}\phantom{\rule{.3em}{0ex}}\mathrm{tan}$
⠞⠁⠝

$\text{hyperbolic tangent,}\phantom{\rule{.3em}{0ex}}\mathrm{tanh}$
⠞⠁⠝⠓

$\text{cotangent,}\phantom{\rule{.3em}{0ex}}\mathrm{cot}\phantom{\rule{.3em}{0ex}}\text{or}\phantom{\rule{.3em}{0ex}}\mathrm{ctn}$
⠉⠕⠞⠀⠕⠗⠀⠉⠞⠝

⠉⠕⠞⠓⠀⠕⠗⠀⠉⠞⠝⠓

$\text{secant,}\phantom{\rule{.3em}{0ex}}\mathrm{sec}$
⠎⠑⠉

$\text{hyperbolic secant,}\phantom{\rule{.3em}{0ex}}\mathrm{sech}$
⠎⠑⠉⠓

$\text{cosecant,}\phantom{\rule{.3em}{0ex}}\mathrm{csc}$
⠉⠎⠉

$\text{hyperbolic cosecant,}\phantom{\rule{.3em}{0ex}}\mathrm{cosh}$
⠉⠎⠉⠓

$\text{maximum,}\phantom{\rule{.3em}{0ex}}\mathrm{max}$
⠍⠁⠭

$\text{minimum,}\phantom{\rule{.3em}{0ex}}\mathrm{min}$
⠍⠊⠝

## Spacing with function names

Function names, or their abbreviations, are not generally preceded by a space unless the space is a naturally occurring one. An example of a naturally occurring space is after a word, or following a symbol that requires a space.

A space must be left after a function name or its abbreviation even if a sign of operation, a letter, or a numeral follows it. Follow the rules for spacing and use of the numeric indicator as if the symbols followed a space naturally.

## Abbreviated function names

Abbreviated function names are not ordinary abbreviations but are mathematical expressions. The rules for their transcription are as follows:

1. No contractions may be used in abbreviated function names, as in sin 35 degrees.
2. Do not use the English letter indicator with a Roman numeral, in regular font type, single letter, or an apparent short-form word contraction following a function name or its abbreviation. For example, is cos y, no English letter indicator is used. Foreign alphabet indicators, such as for Greek letters, may be used following a function name. Refer to Chapter #9 for more information regarding foreign language alphabets and their usage.
3. A space should be left between two abbreviated function names in sequence unless they are clearly unspaced in the print text; for example, log cosine 46 degrees.

If you are in doubt as to whether or not a particular item is an abbreviation or not, treat it as if it is not an abbreviation.

## The use of Braille contractions

As mentioned above, contractions are never used in abbreviated function names. Therefore, as presented previously, the "in" contraction would not be used in as the abbreviation for sine. In unabbreviated function names, however, follow these guidelines regarding contractions:

1. No contractions may be used within an unabbreviated function name in the following circumstances. Use no contractions if the function name is used with related mathematical symbols, with an abbreviated function name, or when joined to another function name with no intervening space. For instance, in example six do not contract the letters i n, since the function name is related to the number of degrees following it. In example five, the contraction was not used since the value within the parentheses, a related mathematical symbol, is associated with it.
2. Contractions may be used in unabbreviated function names if they are not associated with related mathematical symbols, or an abbreviated function name.

## Punctuation used with function names

All abbreviated function names are mathematical expressions. Therefore, they are to be punctuated as mathematical symbols, using the punctuation indicator, dots four five six, for all punctuation other than the comma, hyphen, and dash.

If an unabbreviated function name is used in a mathematical context, it is to be punctuated in the same way as other mathematical symbols. If, however, it is used in literary context, it is to be punctuated according to literary code rules.

If two function names are joined, having no intervening space, then the combination is to be regarded as occurring in a mathematical context.

The contractions for to, into, and by may not be used with abbreviated function names, or with an unabbreviated function name if it is used in a mathematical context.

Function names may have superscripts, subscripts, or other modifications, or the function names may be superscripted or subscripted to other values, letters, or symbols.

Function names may have superscripts, subscripts, or other modifications, or the function names may be superscripted or subscripted to other values, letters, or symbols.

## Parentheses enclosing the argument of a function

An expression, numeral, or letter often is the argument of the function. The function name can be as simple as f(x), g(y), and d(h) or it can indicate an established relationship, as in the trigonometric and logarithmic functions.

### Example 1

a numeral associated with a function name; no space before function name

$3\mathrm{secant}30°$
⠼⠒⠎⠑⠉⠁⠝⠞⠀⠼⠒⠴⠘⠨⠡

### Example 2

function abbreviation followed by a numeral

$5\mathrm{sin}2x$
⠼⠢⠎⠊⠝⠀⠼⠆⠭

### Example 3

function abbreviation following a sign of comparison; space occurs naturally

$1=\mathrm{tan}45°$
⠼⠂⠀⠨⠅⠀⠞⠁⠝⠀⠼⠲⠢⠘⠨⠡

### Example 4

$\frac{1}{\mathrm{tan}A}=\mathrm{cot}A$
⠹⠂⠌⠞⠁⠝⠀⠠⠁⠼⠀⠨⠅⠀⠉⠕⠞⠀⠠⠁

### Example 5

two abbreviated function names unspaced

$\mathrm{arctan}\left(1\right)=\overline{)\phantom{\rule{2em}{2ex}}}$
⠁⠗⠉⠞⠁⠝⠀⠷⠂⠾⠀⠨⠅⠀⠿

### Example 6

$\mathrm{cosine}60°=\frac{1}{2}$
⠉⠕⠎⠊⠝⠑⠀⠼⠖⠴⠘⠨⠡⠀⠨⠅⠀⠹⠂⠌⠆⠼

### Example 7

two joined function names

$\text{What is}\phantom{\rule{.3em}{0ex}}\mathrm{logsine}\text{?}$
⠠⠺⠓⠁⠞⠀⠊⠎⠀⠸⠩⠀⠇⠕⠛⠎⠊⠝⠑⠀⠸⠱⠦

### Example 8

$\text{Is}\phantom{\rule{.3em}{0ex}}\mathrm{sine}\phantom{\rule{.3em}{0ex}}\text{positive in quadrant}\phantom{\rule{.3em}{0ex}}II\text{?}$
⠠⠊⠎⠀⠸⠩⠀⠎⠊⠝⠑⠀⠏⠕⠎⠊⠞⠊⠧⠑⠀⠸⠱⠀⠊⠝⠀⠟⠥⠁⠙⠗⠁⠝⠞⠀⠠⠠⠊⠊⠦

### Example 9

abbreviated function names; use mathematical punctuation; do not use contractions

$\text{Is it}\phantom{\rule{.3em}{0ex}}\mathrm{sin},\phantom{\rule{.3em}{0ex}}\mathrm{cos},\phantom{\rule{.3em}{0ex}}\text{or}\phantom{\rule{.3em}{0ex}}\mathrm{tan}\text{?}$
⠠⠊⠎⠀⠊⠞⠀⠸⠩⠀⠎⠊⠝⠠⠀⠉⠕⠎⠠⠀⠠⠄⠕⠗⠀⠞⠁⠝⠀⠸⠱⠦

### Example 10

unabbreviated function names in a literary setting; use literary punctuation; contractions may be used

$\text{Is it}\phantom{\rule{.3em}{0ex}}\mathrm{sine},\phantom{\rule{.3em}{0ex}}\mathrm{cosine},\phantom{\rule{.3em}{0ex}}\text{or}\phantom{\rule{.3em}{0ex}}\mathrm{tangent}\text{?}$
⠠⠊⠎⠀⠊⠞⠀⠎⠊⠝⠑⠂⠀⠉⠕⠎⠊⠝⠑⠂⠀⠕⠗⠀⠞⠁⠝⠛⠑⠝⠞⠦

### Example 11

joined function names

$\text{Is "logsine" a function?}$
⠠⠊⠎⠀⠸⠩⠀⠦⠇⠕⠛⠎⠊⠝⠑⠴⠀⠸⠱⠀⠁⠀⠋⠥⠝⠉⠞⠊⠕⠝⠦

### Example 12

$\text{This is shown by}\phantom{\rule{.3em}{0ex}}\mathrm{cos}30°\text{.}$
⠠⠞⠓⠊⠎⠀⠊⠎⠀⠎⠓⠕⠺⠝⠀⠃⠽⠀⠸⠩⠀⠉⠕⠎⠀⠼⠒⠴⠘⠨⠡⠀⠸⠱⠲

### Example 13

$\text{It can be converted to}\phantom{\rule{.3em}{0ex}}\mathrm{log}n\text{.}$
⠠⠊⠞⠀⠉⠁⠝⠀⠃⠑⠀⠉⠕⠝⠧⠑⠗⠞⠑⠙⠀⠞⠕⠀⠸⠩⠀⠇⠕⠛⠀⠝⠀⠸⠱⠲

### Example 14

contractions used with unabbreviated function names because they are not in a mathematical context

$\text{Refer to cosines on page 77 in the text.}$
⠠⠗⠑⠋⠑⠗⠀⠞⠕⠀⠉⠕⠎⠊⠝⠑⠎⠀⠕⠝⠀⠏⠁⠛⠑⠀⠼⠛⠛⠀⠊⠝⠀⠞⠓⠑⠀⠞⠑⠭⠞⠲

### Example 15

parentheses enclosing the argument of a trigonometric function

$\mathrm{cos}\left(x\right)$
⠉⠕⠎⠀⠷⠭⠾

### Example 16

parentheses enclosing the arguments in logarithmic notation

$\mathrm{log}\left(3\cdot 2\right)=\mathrm{log}\left(3\right)+\mathrm{log}\left(2\right)$
⠇⠕⠛⠷⠒⠡⠆⠾⠀⠨⠅⠀⠇⠕⠛⠷⠒⠾⠬⠇⠕⠛⠷⠆⠾