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1、ChapterlFunctions(函数)1.Definitionl)Afunction/isarulethatassignstoeachelementxinasetAexactlyoneelement,called/(x),inasetB.2)ThesetAiscalledthedomain(定义域)ofthefunction.3)Therange(值域)offisthesetofallpossiblevaluesasxvariesthroughoutthedomain.Note:f(x)=g(x)o兀一—1Examplef(x)=:——,g(x)=x+l=
2、>/(x)丰g(x)x-2.BasicElementaryFunctions(基本初等函数)1)constantfunctionsfM=c2)powerfunctionsf(x)=xa^03)exponentialfunctions/(x)=ax.a>0,adomain:Rrange:(0,oo)4)logarithmicfunctions/(x)=logt7x,a>(XdH1domain:(0,oo)range:R5)trigonometricfunctionsf(x)=siwcf(x)=cosx/(x)=tarLi/(x)=cotr/(x)=secx
3、f(x)=cscx6)inversetrigonometricfunctionsdomainrangegraphX^)=arcsiiirorsin"1x[-1,1]iiI2
4、B2
5、&ti/(x)=arccosxorcos^x[-1,1][0,7l]y(x)=arctanxortan"1xR(44)22X^)=arccotxorcot"1xR（0,龙）3.DefinitionisdefinedbyGiventwofunctions/andg,thecompositefunction(复合函Note(/ogoh)(x)=ExampleIff(x)=[xandg(
6、无)=-天,findeachfunctionanditsdomain.a)fogb)g©fc)fofd)gogSolutiona)(/。g)(x)=/(g(x))=/(丁2-无)=Jj2—x=勺2-天domain:[xx<2}or(-qo,2]b)(g。/)(x)==g(頁)=一長[x>0,domain:[0,4][2-V7>oc)(f。/)(x)=/(/(x))=/(Vx)=a/x=Vxdomain:[0,oo)d)(g。g)O)=g(g(兀))=g(j2-兀)=』2-J2-兀[2-x>0,<=>domain:[-2,2][2-^2-x>04.Def
7、initionAnelementaryfunction(初等函数)isconstmctedusingcombinations(addition加,subtraction减,multiplication乘，division除)andcompositionstartingwithbasicelementaryfunctions.ExampleF(x)=cos2(x+9)isanelementaryfunction./?(%)=x+9g(x)=cosxf(x)=x2F(x)=/(g(/?(x)))fSinVT_
8、Example/(x)=logdx+isaneleme
9、ntaryfunction・1)PoIynomial(多项式)FunctionsP(x)=anxtl+"+•••++a。xeRwherenisanonnegativeinteger.Theleadingcoefficient(系数)anH0.=>Thedegreeofthepolynomialisn.Inparticular(特别地)，Theleadingcoefficienta。工0.=>constantfunctionTheleadingcoefficientaxH0.=>linearfunctionTheleadingcoefficienta2H()・=
10、>quadratic(二次)functionTheleadingcoefficienta,H0.=>cubic(三次)function2)Rational(有理)Functions3)RootFunctionsExample/(x)=1-xifx<[Xifx>xissuchthatQ(x)H0.}wherePandQarepolynomials.6.Properties(性质)1)Symmetry(对称性)evenfunction:/(-x)=/(兀)，Vxinitsdomain.symmetricw.r.t-(withrespectto关于)they-ax
11、is.oddfunction:/(-x
