аЯрЁБс>ўџ *,ўџџџ)џџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџьЅСM №Пкbjbjт=т= -€W€WЭ џџџџџџlцццццццњ:::8r†њh’ІІІІІІІІцшшшE-Ly LХ $њ Xщ 9цІІІІІщ вццІІ"вввІцІцІцвІцввццццІš Т]‡ ГСњ@:Мцц80hцrвrцвњњццццйFunction Notation or "OK, so f(x) doesn't mean f times x, what does it mean?" The Notation Game We use f(2) to stand for the output that goes with 2 in the f function. The letters f, g, and h are our favorite letters for functions. (Other letters may be used, too.) A function is a rule in which each input has exactly one output. To determine an output all you need is the function, and an input. Say the function is f and input is 2. In mathematics, For example, f(2) = 7, then the input is 2 and the output is 7. Keep in mind that outputs are often y-values, so we may use f(2) to stand for the y-value that we get when x is 2, in the f function. Furthermore, since inputs and outputs are often put into ordered pairs, we may use f(2) to stand for the second coordinate that goes with 2, in the f function. For example, f(2) = 7, then (2,7) is an ordered pair in the f function. f(x) is the output that goes with x in the f function. Note that here, x is a varying quantity. You may think of it as placeholder. Usually, x can take on any of a number of values. For example, if f(x) = 2x+1, then the input is x and the output is 2x+1. If the input is 6 the output is 13. f(6) = 13. So, isn't f(x) just y ? f(8) is the y-value (output) but it also tells which y-value, namely the y-value that goes with 8 in the f function. Often times y does not suffice because there may be lots of x-values and lots of functions. (For example: f(3), g(3), t(3), f(7), t(7), s(7.25).) In some cases, you will find that there are also advantages to using (just) y instead of function notation ("f(x)"). Function Notation in a Different Disguise The same function notation idea is used in many other settings, but since f, g, and h are not used, the similarity if often missed. Three examples: C№ log(x), sin(x), abs(x). With frequently used functions (like logarithm, sine, and absolute value) a shortened form of the name of the function is used instead of f. C№ On an electronic (computer) spreadsheet @ is used to indicate functions. For example, @AVG(2,5,9) means to output the average of 2, 5, and 9. Here, three inputs were needed. C№ Probability. Say a coin is flipped. The function is the probability function. P(heads) = 2 means the input is heads, and the output is 2. Capital P is used instead of f. The idea of a function is central for understanding mathematics, science, and applications of mathematics. Understanding the notation is a key for the understanding of functions. J.R.Olsen ~~ W.I.U. !/078MO`ahlžЈЕКПСЇЈирєі /0GK]^wx†‡‘цъ'(2AIpq|€žŸЇЈФХл  FQefy}ђячяпдпдпдпяпяЮХЮХЮяПяПяПяПяПяПяПяПяХЮХЮХЮХЮяХЮХЮяПяПяПяПяПяИДяПяПяПяПя>*CJ 6>*CJ] 6CJ]56CJ\] 5CJ\56CJ\]aJ5CJ\aJ6CJ]aJCJ5CJOJQJ\^JaJGNOaЉЫ |5БВЪK L v T њњњјјТјјНјјјјјЗЗЎ  „pџ„а„0§]„pџ^„а`„0§„pџdh]„pџ„pџ]„pџdh5„! „й& $d%d&d'd-D .„№/„№MЦ џџџNЦOЦPЦQЦ$a$Тйўў’ ЂІАВМРЦЧЩЪЯжзљўџ   3 4 L M | } Ќ б ! " B F J L u Р Ц Ъ Ы    * 0 Ю J L T V ИКtvав  ТУжзйкњїњїњїяфяфяїњїњїрїњїњїњїњїњїњїњїњїляїњїњїдїњїњїњїрЭїдїдїЦїЦїњїМїї5OJQJ\aJ CJOJQJ 6>*CJ] CJOJQJCJaJ>*CJ56CJ\]aJ5CJ\aJCJ 6CJ]CT И  ТУзийкёёыыцсппы$a$dџ„pџ]„pџ „pџ„а„0§]„pџ^„а`„0§ +0PАа/ Ар=!А "А #€$€%АА А  i@@ёџ@ Normal1$7$8$H$_HaJmH sH tH <A@ђџЁ< Default Paragraph Font4&@ђџё4 Footnote Referenceх џџџџNOaЉЫ |5БВЪKLv Еg  Э Ю т у ц ˜0€€˜0€€˜0€€˜0€€˜0€€˜0€€˜0€€˜0€€˜0€€˜0€€˜0€€˜0€€˜0€€˜0€€˜0€€˜0€€˜0€€˜0€€˜0€€˜0€€˜0€€˜0€€š@0€€˜@0€€˜@0€€ к T к й Э у ц Э у ц џџWIU‚C:\0lsen - everything important\Mathematics Education\Content\Fun (ctions)\TEACHING\Key handouts\word and rtf docs\FUN_NOTATON.docџ@HP LaserJet 4100 PCL 6mathDEPTlpt3:HPBF0420HP LaserJet 4100 PCL 6HP LaserJet 4100 PCL 6mathDEPT”И?€dXXL.HP LaserJet 4100 PCL 6420.PMD2/†xœeЯ.CAЦЯ7чЖуOK#”бP‚……ЈЄUњЖ?šsšоJ4RмЈБ‘x ЕєУЮзмйšХwц7_2ѓ}†џ—Ђ 7ш’,BcвЊс-S xл