基本初等函數(shù)及其圖像

1、1 一、基本初等函數(shù)一、基本初等函數(shù)1.冪函數(shù)冪函數(shù))( 是常數(shù)是常數(shù) xyoxy)1 , 1(112xy xy xy1 xy (11 2 3) 1常用的冪函數(shù)， ， ，222.指數(shù)函數(shù)指數(shù)函數(shù))1, 0( aaayxxay xay)1( )1( a)1 , 0( xey 2.7182818e 33.對數(shù)函數(shù)對數(shù)函數(shù))1, 0(log aaxyalnlogeyxx自然對數(shù)函數(shù)xyalog xya1log )1( a)0 , 1( 44.三角函數(shù)三角函數(shù)正弦函數(shù)正弦函數(shù)xysin xysin 5xycos xycos 余弦函數(shù)余弦函數(shù)6正切函數(shù)正切函數(shù)xytan xytan |,(21)2dx

2、xr xn7xycot 余切函數(shù)余切函數(shù)xycot |,dx xr xn8正割函數(shù)正割函數(shù)1seccosyxxxysec |,(21)2dx xr xn91cscsinyxx余割函數(shù)余割函數(shù)xycsc |,dx xr xn105.反三角函數(shù)反三角函數(shù)xyarcsin xyarcsin 反反正正弦弦函函數(shù)數(shù)rc sinyax11xyarccos xyarccos 反反余余弦弦函函數(shù)數(shù)rc c o syax12xyarctan xyarctan 反正切函數(shù)反正切函數(shù)rc ta nyax13常數(shù)函數(shù)、冪函數(shù)、指數(shù)函數(shù)、對數(shù)函數(shù)、三常數(shù)函數(shù)、冪函數(shù)、指數(shù)函數(shù)、對數(shù)函數(shù)、三角函數(shù)和反三角函數(shù)統(tǒng)稱為角函數(shù)

3、和反三角函數(shù)統(tǒng)稱為基本初等函數(shù)基本初等函數(shù).xycot 反余切函數(shù)反余切函數(shù)arcxycot arcrc c o tyax14二、雙曲函數(shù)與反雙曲函數(shù)二、雙曲函數(shù)與反雙曲函數(shù)2eeshxxx 雙曲正弦雙曲正弦chxy shxy ),(:d奇函數(shù)奇函數(shù).2eechxxx 雙曲余弦雙曲余弦),(:d偶函數(shù)偶函數(shù).1.雙曲函數(shù)雙曲函數(shù)xey21 xey 2115shchxxxxxeethxxee雙曲正切奇函數(shù)奇函數(shù),),(:d有界函數(shù)有界函數(shù),16雙曲函數(shù)常用公式雙曲函數(shù)常用公式;chxshyshxchy)yx(sh ;shxshychxchy)yx(ch ;1xshxch22 ;shxchx2x2

4、sh . xshxchx2ch22 sin()sincoscos sin;xyxyxycos()cos cossin sin;xyxyxy22cossin1;xxsin22sincos ;xxx22cos2cossin.xxx172.反雙曲函數(shù)反雙曲函數(shù)奇函數(shù)奇函數(shù),),(:d.),(內(nèi)內(nèi)單單調(diào)調(diào)增增加加在在 ;arshxy 反雙曲正弦反雙曲正弦).1xxln(arshxy2 arshxy 18.), 1內(nèi)單調(diào)增加內(nèi)單調(diào)增加在在), 1 :d y反雙曲余弦反雙曲余弦archx).1xxln(archxy2 archx y19.11ln21xx )1 , 1(: d奇函數(shù)奇函數(shù),.)1 , 1(內(nèi)單調(diào)增加內(nèi)單調(diào)增加在在 y反雙曲正切反雙曲正切arthxarthxy tanharx y20z. 設(shè)設(shè)0 x，函函數(shù)數(shù)值值21)1(xxxf ，求求函函數(shù)數(shù))0()( xxfy的的解解析析表表達達式式.思考思考21思考題解答思考題解答設(shè)設(shè)ux 1則則 2111uuuf ,112uu 故故)0(.11)(2 xxxxf22z 思考思考下下列列函函數(shù)數(shù)能能否否復(fù)復(fù)合合為為函函數(shù)數(shù))(xgfy ，若若能能，寫寫出出其其解解析析式式、定定義義域域、值值域域,)()1(uufy 2)(xxxgu ,ln)()2(uufy 1sin)( xxgu23思考題解答思考題解答2)()1(xxx