1.第一讲:函数的概念、解析式、定义域和值域

Learn G eneral Se cretary on "two to learn a" stre ngthe ning "four Consci ousnes ses" important speech ca use d a strong reaction in t he country. T ime, watching "red treas ure", the origi n of buildi ng the party back t o power, how t o strengthen s ervice s for the masse s, improve party cohesi on, fighting to become t he grass -roots party members a nd ma sses hot topic. Grass -root s party organizations "two" is to stre ngthe n the s ervice of party members a nd ca dres, t he pi one er spirit. Distribution of grass -root s party orga nizations in a ll walks of people, cl othi ng, s helter, w hi ch belongs to the nerve endi ngs of the party organiza tion and comme nts reputation has a direct perce ption of the mass es. Strengthen the party ahea d of the "pe dal" s pirit; strengt hen t he party members and cadre s "succes s does not have to be me" and "the first to bear hards hips , the last to" s ervice spirit to set the party's positive image am ong the pe ople i s importa nt. Grass -roots party organizati ons "two" is t o clea nse all people not ha ppy not to se e "stereotype s", establi sh the honest faithful, diligent faith for t he pe opl e. No nee d to avoi d menti oni ng that, s ome members of our party can not sta nd the "money," corrosion of temptation, thi n, Xu Zhou, s uch abuse a nd corr upt br iber y, malfeasance borers, a nd rat s. Two, is to clean up, t hin, Xu, Z hou's s oluti on to rest ore the party's fresh a nd natural, s olid a nd honest w ork style. Cleansing "take, eat, card," undesirabl e and be haviour, "cr oss, hard a nd col d, push" attitude. Gras s-r oots party organizati ons "two" is to stre ngthe n the se nse of ordi nary party members, parti cipating i n consci ous nes s, unity cons ciousness. F or reasons k now n, members of grass-r oots party branche s less m obil e, less re sources , and the constructi on of party organi zations have some lag. Tw o studies, i s to focus on the grass-r oots party branche s "loose, s oft, loose" problem, advance the party members and ca dres, "a gang w orking", "Hong Kong re port." Strong cleanup a ctions, style and rambli ng, pre sumpt uous "unqualifie d" party members, pay s special attenti on to party members a nd ca dres "joi ning party of thought" problem. "Party buildi ng" is obtai ned i n the l ong -term development of our party's histori cal experi ence accumul ated. Two i s our party under the new histori cal conditions, stre ngthe n t he party's constr uction of a ne w "rectification movement." Gras s-r oots party organizati ons shoul d always cat ch the hard w ork, res ults-oriente d. Two educational outcome s are long -term orie nted and become a n important impetus for the w ork. "Two" shoul d have thre e kinds of consci ousne ss "two" study and education, ba sic lear ning lie s in the doi ng. Only the Constituti on address t he serie s of party rule s, and do soli d work, be qualified party members ha d a s olid ideol ogical basis . Only the "learni ng" and "do" real unit y, to form a "learn-l earn-do-do" the virtuous cycle, and ultimately achieve the fundamental obje ctive of education. T his req uires that t he Organization

第一讲
一、引言

函数的概念、解析式、定义域和值域

1.本节的地位:函数是整个高中数学的重点,而函数的概念、解析式、定义域和值域 又是研究函数的基本出发点, 对于研究函数的性质和图象有着极其重要的作用, 也是每年高 考试卷必考的内容之一,因此本讲内容在高考中占据十分重要的地位. 2.考纲要求:了解构成函数的要素,会求一些简单函数的定义域和值域;能根据不同 需要选择恰当的方法表示函数;能运用求值域的常用方法解决实际问题和最优问题. 3.考情分析:涉及本讲内容的问题仍将出现在 2010 年高考试题中,函数的概念要求 较低,以函数解析式、定义域的考查为主,题型以选择题和填空题为主.

二、考点梳理
1.函数的概念: 设 A , B 是非空的数集,如果按某种确定的对应关系 f ,使对于集合 A 中的任意一个 数 x ,在集合 B 中都有唯一确定的数 f ? x ? 和它对应,那么就称 f : A ? B 为从集合 A 到集 合 B 的一个函数,记作 y ? f ( x)( x ? A) .其中 x 叫自变量. 2.函数的定义域和值域: 自变量 x 的取值范围 A 叫做函数的定义域,它是构成函数的重要组成部分.一般地, 如果没有特殊标明定义域, 则认为是使函数解析式有意义的自变量的取值范围. 在实际问题 中,函数的定义域还要受到实际意义的限制. 与 x 的值相对应的 y 值叫做函数值. 对于函数 y ? f ? x ?? x ? A? , 函数的值域是由对应 法则 f 对自变量 x 在定义域内取值时相应的函数值的集合.显然值域是集合 B 的子集.

三、典型问题选讲
例1 已知集合 M ? {x | 0 ? x ? 2} , N ? { y | 0 ? y ? 2} ,再给出下列四个图形,其中 )

能表示从集合 M 到集合 N 的函数关系的是(

分析:要从函数的图象体现出从集合 M 到集合 N 的函数关系,应以函数的概念为突破 口.根据函数的定义: “集合 M 中的任一元素,在对应法则 f 作用下,在集合 N 中都有唯
learning e ducation, ne ed thre e kinds of consci ousnes s: one i s to esta blis h an i ntegrated aware ness . "Learni ng" and "do" w hat car isTw o-whe el, bir d wing s, ne ed to g o ha nd i n ha nd, one end ca n be negle cted. Communist theoreti cian a nd ma n. Only by closely combini ng the ory a nd pra ctice t ogether in or der to truly real ize the ir value. " Learni ng" is the F oundation, the Foundati on i s not strong , shaki ng; " "Is the key to net t o net t housands of accounts. 。 泄 宣 值 价 感 情 华 升 结 总 验 经 识 知 活 实 炼 提 头 口 言 语 用 运 句 词 字 对 于 在 现 表 更 性 要 重 它 , 忆 记 和 考 思 象 想 联 、 力 察 观 的 生 学 养 培 能 但 不 作 写 "Two" education, "" lay the ba sis, g oing to " do" the key gri p, s o that the "lear ning" a nd "doing" ba ck to sta ndar d, s o that t he majori ty of party members "learn" lear ning theory of nutrie nts, in t he "doing" pra ctice party's purposes . Second, to e stablis h a se nse of de pth. "Learni ng" and "do" not Chu draw n, entire ly diff erent, but the organi c unity of the w hole . "Two" learni ng educati on, w e nee d to ex plore i ntegrating "learni ng " in "do", exhi bit "do" in "S cience". To avoi d the "lear ning" into simple r oom instructi on, "do" int o a monotone for doing . Should ex ploration "learn" in t he ha s "do", "do" i n the has "learn" of educati on a nd practice of carrie r, makes general grass-r oots members ca n in "lear n" in the has "do" of achiev ements s ens e, in "do" in the has "learn" of get se nse , real makes party of the ory brai n into hea rt, put for people servi ce concept outsi de of Yu sha ped. Third, to adhere to l ong -term the aware nes s. Style constr ucti on on the road foreve r, "two" ha d to catch the l ong -term. "Two" study and education, by no mea ns, a ssault -style wi nd-s port, but the re curre nt educati on wit hin the party. In re cent years , the party's mas s line e ducation practi ce a nd "three -thre e" spe cial educati on i n grass -roots bor ne rich fruits, vast numbers of party member s and cadre s withstood the bapti sm of the s pirit. "Two" greater nee d to focus on longer hold l ong -term, to esta blis h and perfect the effective mechanism of the educati on, focusi ng on the creation of long-term educati on, strive to make the vast number of party members to maintain their va nguard Col or, maintai n the party's adva nce d nature a nd purit y. Awarene ss -raising , antennas a nd atmosphere – a di scussi on on how lea ding ca dres of party members "two" curre nt, "two" activity is in full swing up a nd dow n the country, party cadre s as a "key minority" is bot h a barometer and imp etus. The "two" meani ng enoug h dee p, is to determine t he party ca dres can res olve to study har d first. In the "tw o" in the pr oce ss, s ome ca dres of himse lf, standing l ong, high awar enes s, that Constitution Party rule s is simpl e, its not worth bothering s ome party ca dres thi nk s pea k series ha s not hing to do wit h the grass -roots work , water busine ss lear ning seri es of s peeches s een a s window dressi ng. These "lazy, cas ual, a nd deca dent" idea s learni ng lacks m otivation, a serious impe diment to "two" effect. John Stuart M ill once sa id, only a ba sic el ement of human thoug ht patterns change dramaticall y, human de stiny ca n make great improvement. T he same, only party members and

Learn G eneral Se cretary on "two to learn a" stre ngthe ning "four Consci ousnes ses" important speech ca use d a strong reaction in t he cou ntry. T ime, watching "red treas ure", the origi n of buildi ng the party back t o power, how t o strengthen s ervice s for the masse s, improve party cohesi on, fighting to become t he grass -roots party members a nd ma sses hot topic. Grass -root s party organizations "two" is to stre ngthe n the s ervice of party members a nd ca dres, t he pi one er spirit. Distribution of grass -root s party orga nizatio ns in a ll walks of people, cl othi ng, s helter, w hi ch belongs to the nerve endi ngs of the party organization and comme nts reput ation has a direct perce ption of the mass es. Strengthen the party ahea d of the "pe dal" s pirit; strengt hen t he party members and cadre s "succes s does not have to be me" and "the first to bear hards hips , the last to" s ervice spirit to set the party's posi tive image am ong the pe ople i s importa nt. Grass -roots party organizati ons "two" is t o clea nse all people not ha ppy not to se e "stereotype s", establi sh the honest faithful, diligent faith for t he pe opl e. No nee d to avoi d menti oni ng that, s ome members of our party can not sta nd the "money," corrosion of temptation, thi n, Xu Zhou, s uch abuse a nd corr upt br iber y, malfeasance borers, a nd rats. Two, is to clean up, t hin, Xu, Z hou's s oluti on to rest ore the party's fresh a nd natural, s olid a nd honest w ork style. Cleansing "take, eat, card," undesirabl e and be haviour, "cr oss, hard a nd col d, push" attitude. Gras s-r oots party organizati ons "two" is to stre ngthe n the se nse of ordi nary party members, parti cipating i n consci ous nes s, unity cons ciousness. F or reasons k now n, members of grass-r oots party branche s less m obil e, less re sources , and the constructi on of party organi zations have some lag. Tw o studies, i s to focus on the grass-r oots party branche s "loose, s oft, loose" problem, advance the party members and ca dres, "a gang w orking", "Hong Kong re port." Strong cleanup a ctions, style and rambli ng, pre sumpt uous "unqualifie d" party members, pay s special attenti on to party members a nd ca dres "joi ning party of thought" problem. "Party buildi ng" is obtai ned i n the l ong -term development of our party's histori cal experi ence accumul ated. Two i s our party under the new histori cal conditions, stre ngthe n the party's constr uction of a ne w "rectification movement." Gras s-r oots party organizati ons shoul d always cat ch the hard w ork, res ults-oriente d. Two educational outcome s are long -term orie nted and become a n important impetus for the w ork. "Two" shoul d have thre e kinds of consci ousne ss "two" study and education, ba sic lear ning lie s in the doi ng. Only the Constituti on address t he serie s of party rule s, and do soli d work, be qualified party members ha d a s olid ideol ogical basis . Only the "learni ng" and "do" real unit y, to form a "learn-l earn-do-do" the virtuous cycle, and ultimately achieve the fundamental obje ctive of education. T his requires that t he Organization

一元素与之对应. ”由此逐一进行判断即可. 解:对于图 A: M 中属于 ?1, 2? 的元素,在 N 中没有象,不符合定义; 对于图 B:符合 M 到 N 的函数关系; 对于图 C: M 中有一部分的元素的象不属于集合 N ,因此它不表示 M 到 N 的函数关 系; 对于图 D:其象不唯一,因此也不表示 M 到 N 的函数关系. 由上分析可知,应选 B. 归纳小结: (1)该题考查了函数概念,函数概念的本质是两个集合之间的对应关系,因 此在求解该题时要从定义出发,注意集合 M 中元素的任意性和集合 N 中元素的唯一性,将 这种对应关系与图象结合起来. (2)在问题的解决过程中,将图形语言与代数语言有效地结合并合理转化,因此要注 意培养数形结合的数学思想,提高数学转化能力和抽象思维能力. 例 2 已知下列几组函数,其中表示同一函数的有( ) A.0 个 B.1 个 C.2 个 D.3 个 ① f ? x ? ? x, g ? x ? ? ③ f ? x? ?

x 2 ; ② f ? x ? ? x, g ? x ? ? 3 x 3 ;

x2 ?1 , g ? x ? ? x ? 1 ; ④ f ? x ? ? x ? 1 ? x ? 1, g ? x ? ? x 2 ? 1 ; x ?1
2 2

⑤ f ? x ? ? x ? 2x ?1 , g ?t ? ? t ? 2t ?1 . 分析:根据函数的定义可以判定,两个函数相同,则它们的对应法则、定义域、值域都 相同,因此要从函数的三要素角度进行观察、对比. 解:①中 g ? x ? ? x ,两个函数的解析式不同; ②中 g ? x ? ? x ,所以与 f ? x ? 表示同一函数; ③中 f ? x ? 定义域为 x x ? ?1 ,而 g ? x ? 的定义域为 R ; ④中 f ? x ? 定义域为 x x ? 1 ,而 g ? x ? 的定义域为 x x ? 1或x ? ?1 ; ⑤两个函数的解析式、定义域相同,所以表示同一函数. 所以选择 C. 归纳小结: (1)实际上判断两个函数是否为同一函数,只需看函数的两个要素:定义域 和对应法则. 只有当两个函数的定义域与对应法则都分别相同时, 这两个函数才是同一函数. (2)该题仍涉及的考点是函数概念.在解决问题的过程中注意对概念和定义的灵活运 用,不断提高数学知识的应用和转化能力. (3)第⑤小题易错判断成它们是不同的函数,原因是对函数的概念理解不透.在函数 的定义域及对应法则 f 不变的条件下,自变量变换字母,以至变换成其他字母的表达式,这
2 2 对于函数本身并无影响,比如 f ? x ? ? x ? 1 , f ? t ? ? t ? 1 , f ? u ? 1? ? ? u ? 1? ? 1 ,都
2

?

?

?

?

?

?

可视为同一函数.

learning e ducation, nee d three ki nds of consciousne ss: one i s to establi sh a n integrated aware nes s. "Lear ning" and "do" what car isTwo -w heel, bird wi ngs, need to g o ha nd in hand, one e nd ca n be negle cted. Communist the oreticia n and man. Only by clos ely com bini ng the ory and practi ce togethe r in order to tr uly realize the ir value. "Le arni ng" is the Foundati on, t he Foundati on i s not str ong, s haki ng; " "Is the key to net to net thousa nds of accounts. 。 泄 宣 值 价 感 情 华 升 结 总 验 经 识 知 活 实 炼 提 头 口 言 语 用 运 句 词 字 对 于 在 现 表 更 性 要 重 它 , 忆 记 和 考 思 象 想 联 、 力 察 观 的 生 学 养 培 能 但 不 作 写

"Two" education, "" lay the basi s, goi ng to "do" the key grip, so that t he "learni ng" and "doing" ba ck to standard, so that t he majority of party members "learn" learni ng the ory of nutrie nts, i n the "doing" practi ce party's pur poses. Se cond, to e stablis h a se nse of dept h. " Lear ning" and "do" not Chu drawn, entirely different, but the organi c unity of the whole. "Two" lear ning educati on, we nee d t o expl ore integrating "lear ning" in "do", exhibit "do" in "Scie nce". To avoi d the "learni ng" into sim ple room i nstruction, "do" int o a monotone for

doing . Should expl oration "learn" in the has "do", "do" in the has "learn" of e ducati on a nd practice of carrie r, makes general gras s-roots members can i n "learn" in the has "do" of achi evements s ens e, in "do" in the ha s "learn" of get sense, real makes party of theory brai n into heart, put for people servi ce concept outsi de of Yu s hape d. T hird, to a dhere to long-term the aw arenes s. Style constr ucti on on the r oad forever, "two" had to catch t he long-term. "Two" study and educati on, by no mea ns, as sault -style wind-sport, but the recurrent e ducation withi n the part y. In re cent year s, the party's mass line education pra ctice a nd "three -thre e" spe cial educati on i n grass-r oots bor ne rich fruits, vast numbers of party members and ca dres withstood the bapti sm of the spirit . "Two" greater need to focus on l onger hol d long-term, to esta blis h and perfect the effective mecha nism of the education, focusing on the creation of long-term educati on, strive to make the vast num ber of party members t o maintain their va nguard Col or, maintai n the party's adva nce d nature a nd purit y. Awarene ss -raising , antennas a nd atmosphere – a di scussi on on how lea ding ca dres of party members "two" curre nt, "two" activity is in full swing up a nd dow n the country, party cadre s a s a "key minority" is bot h a barometer and impetus. The "two" meani ng enoug h dee p, is to determine t he party ca dres can res olve to study har d first. In the "tw o" in the pr oce ss, s ome ca dres of himse lf, standing l ong, high awar enes s, that Constitution Party rule s is simpl e, its not worth bothering s ome party ca dres thi nk s pea k series ha s not hing to do wit h the grass -roots work , water busine ss lear ning seri es of s peeches s een a s window dressi ng. These "lazy, cas ual, a nd deca dent" idea s learni ng lacks m otivation, a serious impe diment to "two" effect. John Stuart M ill once sa id, only a ba sic el ement of human thoug ht patterns change dramaticall y, human de stiny ca n make great improvement. T he same, only party members

and

2

Learn G eneral Se cretary on "two to learn a" stre ngthe ning "four Consci ousnes ses" important speech ca use d a strong reaction in t he country. T ime, watching "red treas ure", the origi n of buildi ng the party back t o power, how t o strengthen s ervice s for the masse s, improve party cohesi on, fighting to become t he grass -roots party members a nd ma sses hot topic. Grass -root s party organizations "two" is to stre ngthe n the s ervice of party members a nd ca dres, t he pi one er spirit. Distribution of grass -root s party orga nizations in a ll walks of people, cl othi ng, s helter, w hi ch belongs to the nerve endi ngs of th e party organization and comme nts reputation has a direct perce ption of the mass es. Strengthen the party ahea d of the "pe dal" s pirit; strengt hen t he party members and cadre s "succes s does not have to be me" and "the first to bear hards hips , the last to" s ervice spirit to set the party's positive image am ong the pe ople i s importa nt. Grass -roots party organizati ons "two" is t o clea nse all people not ha ppy not to se e "stereotype s", establi sh the honest faithful, diligent faith for t he pe opl e. No nee d to avoi d menti oni ng that, s ome members of our party can not sta nd the "money," corrosion of temptation, thi n, Xu Zhou, s uch abuse a nd corr upt br iber y, malfeasance borers, a nd rats. Two, is to clean up, t hin, Xu, Z hou's s oluti on to rest ore the party's fresh a nd natural, s olid a nd honest w ork style. Cleansing "take, eat, card," undesirabl e and be haviour, "cr oss, hard a nd col d, push" attitude. Gras s-r oots party organizati ons "two" is to stre ngthe n the se nse of ordi nary party members, parti cipating i n consci ous nes s, unity cons ciousness. F or reasons k now n, members of grass-r oots party branche s less m obil e, less re sources , and the constructi on of party organi zations have some lag. Tw o studies, i s to focus on the grass-r oots party branche s "loose, s oft, loose" problem , advance the party members and ca dres, "a gang w orking", "Hong Kong re port." Strong cleanup a ctions, style and rambli ng, pre sumpt uous "unqualifie d" party members, pay s special attenti on to party members a nd ca dres "joi ning party of thought" problem. "Party buildi ng" is obtai ned i n the l ong -term development of our party's histori cal experi ence accumul ated. Two i s our party under the new histori cal conditions, stre ngthe n the party's constr uction of a ne w "rectification movement." Gras s-r oots party organizati ons shoul d always cat ch the hard w ork, res ults-oriente d. Two educational outcome s are long -term orie nted and become a n important impetus for the w ork. "Two" shoul d have thre e kinds of consci ousne ss "two" study and education, ba sic lear ning lie s in the doi ng. Only the Constituti on address t he serie s of party rule s, and do soli d work, be qualified party members ha d a s olid ideol ogical basis . Only the "learni ng" and "do" real unit y, to form a "learn-l earn-do-do" the virtuous cycle, and ultimately achieve the fundamental obje ctive of education. T his requires that t he Organization

例 3

?1 2 ? ? x , ? x ? 0? ? , ? x ? 0? ① 已 知 两 个 函 数 f ? x? ? ? , g ? x? ? ? x 当 x ? 0 时,求 ? x , x ? 0 ? ? 2 ? ? x , ? x ? 0? ? ?

f? ? g ? x ?? ?及g? ? f ? x ?? ? 的解析式;
分析:由于函数 f ? ? g ? x ?? ?和g? ? f ? x ?? ? 中的变元成为 g ? x ? 和 f ? x ? ,所以只需要进行 代换即可. 解:∵ x ? 0 , ∴f ? ? g ? x ?? ?? f x

? ? ? ?x ?
2

2 2

1 ? x4 , g ? ? f ? x ?? ? ? g ??x? ? ? x .

②已知 f ( x ? 1) ? x 2 ? 5x ? 4 ,求 f ? x ? 的解析式; 分析: f 的作用下变元是 x ? 1 ,因此只需把 x ? 1 看成是整体,通过配凑的方式把解析 式中的变元转化为 x ? 1 的形式,或仍将 x 视为变元,通过换元得到关于 x 的解析式.
2 解法一:∵ f ( x ? 1) ? x ? 5 x ? 4 ? ? x ? 1? ? 7 ? x ? 1? ? 10 ,∴ f ? x ? ? x2 ? 7 x ? 10 . 2 2 解法二:令 x ? 1 ? t ,则 x ? t ? 1 ,∴ f ? t ? ? ? t ? 1? ? 5 ? t ? 1? ? 4 ? t ? 7t ? 10 . 2

∴ f ? x ? ? x ? 7 x ? 10 .
2

③已知 2 f ? x ? ? f ?

?1? x ? ? 10 ,求 f ? x ? 的解析式. ? x? ?1? x ? ? 10 . ? x?
1

解:由 2 f ? x ? ? f ?



可得 2 f ?

?1? x ? ? f ? x ? ? 10 . ? x?
2 x 1 1 ?10 ? ?10 x . 3 3



由①②解得 f ? x ? ?

归纳小结: (1)该题主要考查了函数的解析式的求解方法,能灵活地根据题目条件选择 恰当地方法得到函数的解析式,其中涉及多种数学思想,如函数与方程的思想、分类讨论思 想等,注重对分析问题和解决问题能力的考查. (2)根据已知条件求函数的解析式常用待定系数法、换元法、配方法、赋值法、解方 程组法等. ①当所求函数的解析式的形式已知(如二次函数、指数函数等)常用待定系数法. ②已知 f ? ? g ? x ?? ? 的表达式,求 f ? x ? 的表达式,常用配方法或换元法. ③由简单的函数方程求函数的表达式,常用赋值法及解方程组法.
learning e ducation, nee d three ki nds of consciousne ss: one i s to establi sh a n integrated aware nes s. "Lear ning" and "do" what car isTwo -w heel, bird wi ngs, need to g o ha nd in hand, one e nd ca n be negle cted. Communist the oreticia n and man. Only by clos ely com bini ng the ory and practi ce togethe r in order to tr uly realize the ir value. "Le arni ng" is the Foundati on, t he Foundati on i s not str ong, s haki ng; " "Is the key to net to net thousa nds of accounts. 。 泄 宣 值 价 感 情 华 升 结 总 验 经 识 知 活 实 炼 提 头 口 言 语 用 运 句 词 字 对 于 在 现 表 更 性 要 重 它 , 忆 记 和 考 思 象 想 联 、 力 察 观 的 生 学 养 培 能 但 不 作 写 "Two" education, "" lay the basi s, goi ng to "do" the key grip, so that t he "learni ng" and "doing" ba ck to standard, so that t he majority of party members "learn" learni ng the ory of nutrie nts, i n the "doing" practi ce party's pur poses. Se cond, to e stablis h a se nse of dept h. "Lear ning" and "do" not Chu drawn, entirely different, but the organi c unity of the whole. "Two" lear ning educati on, we nee d to expl ore integrating "lear ning" in "do", exhibit "do" in "Scie nce". To avoi d the "learni ng" into sim ple room i nstruction, "do" int o a monotone for

doing . Should expl oration "learn" in the has "do", "do" in the has "learn" of e ducati on a nd practice of carrie r, makes general gras s-roots members can i n "learn" in the has "do" of achi evements s ens e, in "do" in the ha s "learn" of get sense, real makes party of theory brai n into heart, put for people servi ce concept outsi de of Yu s hape d. T hird, to a dhere to long-term the aw arenes s. Style constr ucti on on the r oad forever, "two" had to catch t he long-term. "Two" study and educati on, by no mea ns, as sault -style wind-sport, but the recurrent e ducation withi n the part y. In re cent year s, the party's mass line education pra ctice a nd "three -thre e" spe cial educati on i n grass-r oots bor ne rich fruits, vast numbers of party members and ca dres withstood the bapti sm of the spirit . "Two" greater need to focus on l onger hol d long-term, to esta blis h and perfect the effective mecha nism of the education, focusing on the creation of long-term educati on, strive to make the vast num ber of party members t o maintain their va nguard Col or, maintai n the party's adva nce d nature a nd purit y. Awarene ss -raising , antennas a nd atmosp here – a di scussi on on how lea ding ca dres of party members "two" curre nt, "two" activity is in full swing up a nd dow n the country, party cadre s as a "key minority" is bot h a barometer and impetus. The "two" meani ng enoug h dee p, is to determine t he party ca dres can res olve to study har d first. In the "tw o" in the pr oce ss, s ome ca dres of himse lf, standing l ong, high awar enes s, that Constitution Party rule s is simpl e, its not worth bothering s ome party ca dres thi nk s pea k series ha s not hing to do wit h the grass -roots work , water busine ss lear ning seri es of s peeches s een a s window dressi ng. These "lazy, cas ual, a nd deca dent" idea s learni ng lacks m otivation, a serious impe diment to "two" effect. John Stuart M ill once sa id, only a ba sic el ement of human thoug ht patterns change dramaticall y, human de stiny ca n make great improvement. T he same, only party members

and

3

Learn G eneral Se cretary on "two to learn a" stre ngthe ning "four Consci ousnes ses" important speech ca use d a strong reaction in t he cou ntry. T ime, watching "red treas ure", the origi n of buildi ng the party back t o power, how t o strengthen s ervice s for the masse s, improve party cohesi on, fighting to become t he grass -roots party members a nd ma sses hot topic. Grass -root s party organizations "two" is to stre ngthe n the s ervice of party members a nd ca dres, t he pi one er spirit. Distribution of grass -root s party orga nizatio ns in a ll walks of people, cl othi ng, s helter, w hi ch belongs to the nerve endi ngs of the party organization and comme nts reput ation has a direct perce ption of the mass es. Strengthen the party ahea d of the "pe dal" s pirit; strengt hen t he party members and cadre s "succes s does not have to be me" and "the first to bear hards hips , the last to" s ervice spirit to set the party's posi tive image am ong the pe ople i s importa nt. Grass -roots party organizati ons "two" is t o clea nse all people not ha ppy not to se e "stereotype s", establi sh the honest faithful, diligent faith for t he pe opl e. No nee d to avoi d menti oni ng that, s ome members of our party can not sta nd the "money," corrosion of temptation, thi n, Xu Zhou, s uch abuse a nd corr upt br iber y, malfeasance borers, a nd rats. Two, is to clean up, t hin, Xu, Z hou's s oluti on to rest ore the party's fresh a nd natural, s olid a nd honest w ork style. Cleansing "take, eat, card," undesirabl e and be haviour, "cr oss, hard a nd col d, push" attitude. Gras s-r oots party organizati ons "two" is to stre ngthe n the se nse of ordi nary party members, parti cipating i n consci ous nes s, unity cons ciousness. F or reasons k now n, members of grass-r oots party branche s less m obil e, less re sources , and the constructi on of party organi zations have some lag. Tw o studies, i s to focus on the grass-r oots party branche s "loose, s oft, loose" problem, advance the party members and ca dres, "a gang w orking", "Hong Kong re port." Strong cleanup a ctions, style and rambli ng, pre sumpt uous "unqualifie d" party members, pay s special attenti on to party members a nd ca dres "joi ning party of thought" problem. "Party buildi ng" is obtai ned i n the l ong -term development of our party's histori cal experi ence accumul ated. Two i s our party under the new histori cal conditions, stre ngthe n the party's constr uction of a ne w "rectification movement." Gras s-r oots party organizati ons shoul d always cat ch the hard w ork, res ults-oriente d. Two educational outcome s are long -term orie nted and become a n important impetus for the w ork. "Two" shoul d have thre e kinds of consci ousne ss "two" study and education, ba sic lear ning lie s in the doi ng. Only the Constituti on address t he serie s of party rule s, and do soli d work, be qualified party members ha d a s olid ideol ogical basis . Only the "learni ng" and "do" real unit y, to form a "learn-l earn-do-do" the virtuous cycle, and ultimately achieve the fundamental obje ctive of education. T his requires that t he Organization

例 4( 2007 年安徽卷)如图所示中的图象所表示的函数的解析式为(



3 | x ? 1| ? 0 ? x ? 2 ? 2 3 C. y ? ? | x ? 1| ? 0 ? x ? 2 ? 2
A. y ?

B. y ?

3 3 ? | x ? 1| ? 0 ? x ? 2 ? 2 2

D. y ? 1? | x ?1| ? 0 ? x ? 2?

分析:本题是由图形判断函数的解析式,由于图象在定义域 ?0,1? , ?1, 2? 都是线段,因此 其解析式都是一次函数型,利用待定系数法,分别求出各定义域上的解析式即可.另外在图 象上给出了三个特殊点 ? 0, 0 ? , ?1, ? , ? 2, 0 ? ,所以还可以考虑特殊值法. 解:由图象可知,当 0 ? x ? 1 时, y ? ∴y?

? 3? ? 2?

3 3 x ;当 1 ? x ? 2 时, y ? 3 ? x ; 2 2

3 3 ? x ?1 , 0 ? x ? 2 . 2 2

∴应选 B.

另解: (特殊值法)分别代入 x ? 0, x ? 1 进行验证,只有选项 B 符合条件. 归纳小结: (1)本题考查了函数解析式与图象之间的关系,和分段函数解析式的表达形 式,考查了数形结合思想和灵活解题能力. (2) 根据图象求函数解析式或判断函数性质, 要注意在不同的函数自变量的取值范围 内采用恰当的方法求出函数解析式. 如果所求结果能用一个解析式综合, 则应写成一个解析 式的形式,否则应采用分段函数形式. (3)特殊值法的使用可以简化计算过程,降低难度,因此要注意使用.
2 2 例 5 ( 2008 湖 北 卷 ) 已 知 函 数 f ( x) ? x ? 2x ? a , f (bx) ? 9 x ? 6 x ? 2 , 其 中

x ? R , a , b 为常数,则方程 f (ax ? b) ? 0 的解集为



分析:利用待定系数法确定 a , b 的值,确定方程 f (ax ? b) ? 0 形式,从而求解. 解:∵ f ( x) ? x ? 2x ? a ,
2

∴ f (bx) ? b x ? 2bx ? a .
2 2
learning e ducation, nee d three ki nds of consciousne ss: one i s to establi sh a n integrated aware nes s. "Lear ning" and "do" what car isTwo -w heel, bird wi ngs, need to g o ha nd in hand, one e nd ca n be negle cted. Communist the oreticia n and man. Only by clos ely com bini ng the ory and practi ce togethe r in order to tr uly realize the ir value. "Le arni ng" is the Foundati on, t he Foundati on i s not str ong, s haki ng; " "Is the key to net to net thousa nds of accounts. 。 泄 宣 值 价 感 情 华 升 结 总 验 经 识 知 活 实 炼 提 头 口 言 语 用 运 句 词 字 对 于 在 现 表 更 性 要 重 它 , 忆 记 和 考 思 象 想 联 、 力 察 观 的 生 学 养 培 能 但 不 作 写 "Two" education, "" lay the basi s, goi ng to "do" the key grip, so that t he "learni ng" and "doing" ba ck to standard, so that t he majority of party members "learn" learni ng the ory of nutrie nts, i n the "doing" practi ce party's pur poses. Se cond, to e stablis h a se nse of dept h. " Lear ning" and "do" not Chu drawn, entirely different, but the organi c unity of the whole. "Two" lear ning educati on, we nee d t o expl ore integrating "lear ning" in "do", exhibit "do" in "Scie nce". To avoi d the "learni ng" into sim ple room i nstruction, "do" int o a monotone for doing . Should expl oration "learn" in the has "do", "do" in the has "learn" of e ducati on a nd practice of carrie r, makes general gras s-roots members can i n "learn" in the has "do" of achi evements s ens e, in "do" in the ha s "learn" of get sense, real makes party of theory brai n into heart, put for people servi ce concept outsi de of Yu s hape d. T hird, to a dhere to long-term the aw arenes s. Style constr ucti on on the r oad forever, "two" had to catch t he long-term. "Two" study and educati on, by no mea ns, as sault -style wind-sport, but the recurrent e ducation withi n the part y. In re cent year s, the party's mass line education pra ctice a nd "three -thre e" spe cial educati on i n grass-r oots bor ne rich fruits, vast numbers of party members and ca dres withstood the bapti sm of the spirit . "Two" greater need to focus on l onger hol d long-term, to esta blis h and perfect the effective mecha nism of the education, focusing on the creation of long-term educati on, strive to make the vast num ber of party members t o maintain their va nguard Col or, maintai n the party's adva nce d nature a nd purit y. Awarene ss -raising , antennas a nd atmosphere – a di scussi on on how lea ding ca dres of party members "two" curre nt, "two" activity is in full swing up a nd dow n the country, party cadre s a s a "key minority" is bot h a barometer and impetus. The "two" meani ng enoug h dee p, is to determine t he party ca dres can res olve to study har d first. In the "tw o" in the pr oce ss, s ome ca dres of himse lf, standing l ong, high awar enes s, that Constitution Party rule s is simpl e, its not worth bothering s ome party ca dres thi nk s pea k series ha s not hing to do wit h the grass -roots work , water busine ss lear ning seri es of s peeches s een a s window dressi ng. These "lazy, cas ual, a nd deca dent" idea s learni ng lacks m otivation, a serious impe diment to "two" effect. John Stuart M ill once sa id, only a ba sic el ement of human thoug ht patterns change dramaticall y, human de stiny ca n make great improvement. T he same, only party members

and

4

Learn G eneral Se cretary on "two to learn a" stre ngthe ning "four Consci ousnes ses" important speech ca use d a strong reaction in t he country. T ime, watching "red treas ure", the origi n of buildi ng the party back t o power, how t o strengthen s ervice s for the masse s, improve party cohesi on, fighting to become t he grass -roots party members a nd ma sses hot topic. Grass -root s party organizations "two" is to stre ngthe n the s ervice of party members a nd ca dres, t he pi one er spirit. Distribution of grass -root s party orga nizations in a ll walks of people, cl othi ng, s helter, w hi ch belongs to the nerve endi ngs of th e party organization and comme nts reputation has a direct perce ption of the mass es. Strengthen the party ahea d of the "pe dal" s pirit; strengt hen t he party members and cadre s "succes s does not have to be me" and "the first to bear hards hips , the last to" s ervice spirit to set the party's positive image am ong the pe ople i s importa nt. Grass -roots party organizati ons "two" is t o clea nse all people not ha ppy not to se e "stereotype s", establi sh the honest faithful, diligent faith for t he pe opl e. No nee d to avoi d menti oni ng that, s ome members of our party can not sta nd the "money," corrosion of temptation, thi n, Xu Zhou, s uch abuse a nd corr upt br iber y, malfeasance borers, a nd rats. Two, is to clean up, t hin, Xu, Z hou's s oluti on to rest ore the party's fresh a nd natural, s olid a nd honest w ork style. Cleansing "take, eat, card," undesirabl e and be haviour, "cr oss, hard a nd col d, push" attitude. Gras s-r oots party organizati ons "two" is to stre ngthe n the se nse of ordi nary party members, parti cipating i n consci ous nes s, unity cons ciousness. F or reasons k now n, members of grass-r oots party branche s less m obil e, less re sources , and the constructi on of party organi zations have some lag. Tw o studies, i s to focus on the grass-r oots party branche s "loose, s oft, loose" problem , advance the party members and ca dres, "a gang w orking", "Hong Kong re port." Strong cleanup a ctions, style and rambli ng, pre sumpt uous "unqualifie d" party members, pay s special attenti on to party members a nd ca dres "joi ning party of thought" problem. "Party buildi ng" is obtai ned i n the l ong -term development of our party's histori cal experi ence accumul ated. Two i s our party under the new histori cal conditions, stre ngthe n the party's constr uction of a ne w "rectification movement." Gras s-r oots party organizati ons shoul d always cat ch the hard w ork, res ults-oriente d. Two educational outcome s are long -term orie nted and become a n important impetus for the w ork. "Two" shoul d have thre e kinds of consci ousne ss "two" study and education, ba sic lear ning lie s in the doi ng. Only the Constituti on address t he serie s of party rule s, and do soli d work, be qualified party members ha d a s olid ideol ogical basis . Only the "learni ng" and "do" real unit y, to form a "learn-l earn-do-do" the virtuous cycle, and ultimately achieve the fundamental obje ctive of education. T his requires that t he Organization

∵ f (bx) ? 9 x2 ? 6 x ? 2 , ∴ a ? 2, b ? ?3 .
2 ∴ f (ax ? b) ? f ? 2 x ? 3? ? ? 2 x ? 3? ? 2 ? 2 x ? 3? ? 2 ? 4 x ? 8 x ? 5 ? 0 . 2

∵ ? ? 64 ? 4 ? 20 ? 0 , ∴方程 f (ax ? b) ? 0 的解集为 ? . 归纳小结: (1)本题考查了函数的待定系数法求函数的解析式、二次方程的解法的知识 点,考查计算和推理能力. (2)运用待定系数法求含参数解析式中,要注意恒等代数式两边对应系数相等,从而 确定参数. 例6 ( 2008 湖北卷) 函数 f ( x) ? A.(??, ?4] [2, ??)

1 ln( x 2 ? 3x ? 2 ? ? x 2 ? 3x ? 4) 的定义域为 ( x



B.(?4,0)

(0.1)

C.[-4,0)

(0,1]

D.[?4,0)

(0,1)

分析:由于函数的解析式已经明确,并且没有特殊标明定义域,所以定义域为使函数解 析式有意义的自变量的取值范围.

? x 2 ? 3x ? 2 ? 0 ? 2 ?? x ? 3x ? 4 ? 0 解: ? ,可解得函数定义域为 [?4,0) (0,1) . 2 2 x ? 3 x ? 2 ? ? x ? 3 x ? 4 ? 0 ? ?x ? 0 ?
归纳小结: (1)本题考查了函数定义域的意义和基本解法,考查了分析问题和解决问 题的能力.尤其是利用 x2 ? 3x ? 2 ? ?x2 ? 3x ? 4 ? 0 对特殊点 x ? 1 的验证,考查了思 维的全面性. (2)若已知函数解析式,且没有特别要求定义域,则函数的定义域是使函数解析式有 意义的自变量的取值范围. 当 f ? x ? 是整式时,定义域是全体实数; 当 f ? x ? 是分式函数时,定义域是使分母不为零的一切实数; 当 f ? x ? 是偶次根式时,定义域是使被开方式为非负实数的集合; 当 f ? x ? 是对数函数时,满足真数大于零;当对数或指数函数的底数中含参数时,底数 须大于零且不等于 1; 在 y ? tan x 中 x ?

?
2

? k? ? k ? Z ? ;在 y ? cot x 中 x ? k? ? k ? Z ? ;

零指数幂的底数不能为零. 注意:在实际问题中,函数的定义域要受到实际意义的限制.
learning e ducation, nee d three ki nds of consciousne ss: one i s to establi sh a n integrated aware nes s. "Lear ning" and "do" what car isTwo -w heel, bird wi ngs, need to g o ha nd in hand, one e nd ca n be negle cted. Communist the oreticia n and man. Only by clos ely com bini ng the ory and practi ce togethe r in order to tr uly realize the ir value. "Le arni ng" is the Foundati on, t he Foundati on i s not str ong, s haki ng; " "Is the key to net to net thousa nds of accounts. 。 泄 宣 值 价 感 情 华 升 结 总 验 经 识 知 活 实 炼 提 头 口 言 语 用 运 句 词 字 对 于 在 现 表 更 性 要 重 它 , 忆 记 和 考 思 象 想 联 、 力 察 观 的 生 学 养 培 能 但 不 作 写 "Two" education, "" lay the basi s, goi ng to "do" the key grip, so that t he "learni ng" and "doing" ba ck to standard, so that t he majority of party members "learn" learni ng the ory of nutrie nts, i n the "doing" practi ce party's pur poses. Se cond, to e stablis h a se nse of dept h. "Lear ning" and "do" not Chu drawn, entirely different, but the organi c unity of the whole. "Two" lear ning educati on, we nee d to expl ore integrating "lear ning" in "do", exhibit "do" in "Scie nce". To avoi d the "learni ng" into sim ple room i nstruction, "do" int o a monotone for

doing . Should expl oration "learn" in the has "do", "do" in the has "learn" of e ducati on a nd practice of carrie r, makes general gras s-roots members can i n "learn" in the has "do" of achi evements s ens e, in "do" in the ha s "learn" of get sense, real makes party of theory brai n into heart, put for people servi ce concept outsi de of Yu s hape d. T hird, to a dhere to long-term the aw arenes s. Style constr ucti on on the r oad forever, "two" had to catch t he long-term. "Two" study and educati on, by no mea ns, as sault -style wind-sport, but the recurrent e ducation withi n the part y. In re cent year s, the party's mass line education pra ctice a nd "three -thre e" spe cial educati on i n grass-r oots bor ne rich fruits, vast numbers of party members and ca dres withstood the bapti sm of the spirit . "Two" greater need to focus on l onger hol d long-term, to esta blis h and perfect the effective mecha nism of the education, focusing on the creation of long-term educati on, strive to make the vast num ber of party members t o maintain their va nguard Col or, maintai n the party's adva nce d nature a nd purit y. Awarene ss -raising , antennas a nd atmosp here – a di scussi on on how lea ding ca dres of party members "two" curre nt, "two" activity is in full swing up a nd dow n the country, party cadre s as a "key minority" is bot h a barometer and impetus. The "two" meani ng enoug h dee p, is to determine t he party ca dres can res olve to study har d first. In the "tw o" in the pr oce ss, s ome ca dres of himse lf, standing l ong, high awar enes s, that Constitution Party rule s is simpl e, its not worth bothering s ome party ca dres thi nk s pea k series ha s not hing to do wit h the grass -roots work , water busine ss lear ning seri es of s peeches s een a s window dressi ng. These "lazy, cas ual, a nd deca dent" idea s learni ng lacks m otivation, a serious impe diment to "two" effect. John Stuart M ill once sa id, only a ba sic el ement of human thoug ht patterns change dramaticall y, human de stiny ca n make great improvement. T he same, only party members

and

5

Learn G eneral Se cretary on "two to learn a" stre ngthe ning "four Consci ousnes ses" important speech ca use d a strong reaction in t he cou ntry. T ime, watching "red treas ure", the origi n of buildi ng the party back t o power, how t o strengthen s ervice s for the masse s, improve party cohesi on, fighting to become t he grass -roots party members a nd ma sses hot topic. Grass -root s party organizations "two" is to stre ngthe n the s ervice of party members a nd ca dres, t he pi one er spirit. Distribution of grass -root s party orga nizatio ns in a ll walks of people, cl othi ng, s helter, w hi ch belongs to the nerve endi ngs of the party organization and comme nts reput ation has a direct perce ption of the mass es. Strengthen the party ahea d of the "pe dal" s pirit; strengt hen t he party members and cadre s "succes s does not have to be me" and "the first to bear hards hips , the last to" s ervice spirit to set the party's posi tive image am ong the pe ople i s importa nt. Grass -roots party organizati ons "two" is t o clea nse all people not ha ppy not to se e "stereotype s", establi sh the honest faithful, diligent faith for t he pe opl e. No nee d to avoi d menti oni ng that, s ome members of our party can not sta nd the "money," corrosion of temptation, thi n, Xu Zhou, s uch abuse a nd corr upt br iber y, malfeasance borers, a nd rats. Two, is to clean up, t hin, Xu, Z hou's s oluti on to rest ore the party's fresh a nd natural, s olid a nd honest w ork style. Cleansing "take, eat, card," undesirabl e and be haviour, "cr oss, hard a nd col d, push" attitude. Gras s-r oots party organizati ons "two" is to stre ngthe n the se nse of ordi nary party members, parti cipating i n consci ous nes s, unity cons ciousness. F or reasons k now n, members of grass-r oots party branche s less m obil e, less re sources , and the constructi on of party organi zations have some lag. Tw o studies, i s to focus on the grass-r oots party branche s "loose, s oft, loose" problem, advance the party members and ca dres, "a gang w orking", "Hong Kong re port." Strong cleanup a ctions, style and rambli ng, pre sumpt uous "unqualifie d" party members, pay s special attenti on to party members a nd ca dres "joi ning party of thought" problem. "Party buildi ng" is obtai ned i n the l ong -term development of our party's histori cal experi ence accumul ated. Two i s our party under the new histori cal conditions, stre ngthe n the party's constr uction of a ne w "rectification movement." Gras s-r oots party organizati ons shoul d always cat ch the hard w ork, res ults-oriente d. Two educational outcome s are long -term orie nted and become a n important impetus for the w ork. "Two" shoul d have thre e kinds of consci ousne ss "two" study and education, ba sic lear ning lie s in the doi ng. Only the Constituti on address t he serie s of party rule s, and do soli d work, be qualified party members ha d a s olid ideol ogical basis . Only the "learni ng" and "do" real unit y, to form a "learn-l earn-do-do" the virtuous cycle, and ultimately achieve the fundamental obje ctive of education. T his requires that t he Organization

例7 定义域.

设函数 y ? f ? x ? 的定义域为 ?0,1? , 求函数 F ? x ? ? f ? x ? a ? ? f ? x ? a ?? a ? 0? 的

分析: 该题已知函数 y ? f ? x ? 的定义域, 求含有参数的解析式的定义域, 显然要对 a 进 行分类讨论. 由于函数 f ? x ? 是抽象函数, 所以在求函数 f ? x ? a ? 和 f ? x ? a ? 的定义域时, 把握在 f 的作用下,括号里的变元范围相同.在分别求出 f ? x ? a ? 和 f ? x ? a ? 定义域的基 础上,求 F ? x ? 的定义域是根据 a 的范围求出的交集. 解:由 ?

?0 ? x ? a ? 1, ? ? a ? x ? 1 ? a, 得? ?0 ? x ? a ? 1, ?a ? x ? 1 ? a.

∵ a ? 0 ,∴ ?a ? a,1 ? a ? 1 ? a .

1 1 时, x ? ; 2 2 1 (2)当 1 ? a ? a ,即 a ? 时, a ? x ? 1 ? a . 2 1 ∴当 0 ? a ? 时, F ? x ? 的定义域为 ? a,1 ? a? . 2
(1)当 1 ? a ? a ,即 a ? 归纳小结: (1)该题考查了抽象函数定义域,体现了对分类讨论思想和逆向思维能力的 考查. (2)求复合函数的定义域:若已知 f ? ? g ? x ?? ? 的定义域为 x ?? a, b? ,求 f ? x ? 的定义 域只需利用 a ? x ? b ,求出 g ? x ? 的范围,而 g ? x ? 的范围就是 f ? x ? 的定义域;若已知 求f ? 只需由 a ? g ? x ? ? b , 求出 x 的范围, f ? x ? 的定义域为 x ?? a, b? , ? ?? ?g x ? 的定义域, 即为 f ? ? g ? x? ? ? 的定义域.在某些情况下,也可以先求出函数的解析式,由解析式求出

f? ? g ? x ?? ? 的定义域.
求运算型解析式的定义域:当 f ? x ? 是由有限个基本初等函数的四则运算而合成的函数 时,则其定义域一般是各基本初等函数的定义域的交集. 例 8( 2007 年北京卷)已知函数 f ?x ?, g ?x ? 分别由下表给出:

则 f ?g ?1?? 的值
6

;满足 f ?g ?x ?? ? g ? f ?x ??的 x 的值



learning e ducation, nee d three ki nds of consciousne ss: one i s to establi sh a n integrated aware nes s. "Lear ning" and "do" what car isTwo -w heel, bird wi ngs, need to g o ha nd in hand, one e nd ca n be negle cted. Communist the oreticia n and man. Only by clos ely com bini ng the ory and practi ce togethe r in order to tr uly realize the ir value. "Le arni ng" is the Foundati on, t he Foundati on i s not str ong, s haki ng; " "Is the key to net to net thousa nds of accounts. 。 泄 宣 值 价 感 情 华 升 结 总 验 经 识 知 活 实 炼 提 头 口 言 语 用 运 句 词 字 对 于 在 现 表 更 性 要 重 它 , 忆 记 和 考 思 象 想 联 、 力 察 观 的 生 学 养 培 能 但 不 作 写

"Two" education, "" lay the basi s, goi ng to "do" the key grip, so that t he "learni ng" and "doing" ba ck to standard, so that t he majority of party members "learn" learni ng the ory of nutrie nts, i n the "doing" practi ce party's pur poses. Se cond, to e stablis h a se nse of dept h. " Lear ning" and "do" not Chu drawn, entirely different, but the organi c unity of the whole. "Two" lear ning educati on, we nee d t o expl ore integrating "lear ning" in "do", exhibit "do" in "Scie nce". To avoi d the "learni ng" into sim ple room i nstruction, "do" int o a monotone for

doing . Should expl oration "learn" in the has "do", "do" in the has "learn" of e ducati on a nd practice of carrie r, makes general gras s-roots members can i n "learn" in the has "do" of achi evements s ens e, in "do" in the ha s "learn" of get sense, real makes party of theory brai n into heart, put for people servi ce concept outsi de of Yu s hape d. T hird, to a dhere to long-term the aw arenes s. Style constr ucti on on the r oad forever, "two" had to catch t he long-term. "Two" study and educati on, by no mea ns, as sault -style wind-sport, but the recurrent e ducation withi n the part y. In re cent year s, the party's mass line education pra ctice a nd "three -thre e" spe cial educati on i n grass-r oots bor ne rich fruits, vast numbers of party members and ca dres withstood the bapti sm of the spirit . "Two" greater need to focus on l onger hol d long-term, to esta blis h and perfect the effective mecha nism of the education, focusing on the creation of long-term educati on, strive to make the vast num ber of party members t o maintain their va nguard Col or, maintai n the party's adva nce d nature a nd purit y. Awarene ss -raising , antennas a nd atmosphere – a di scussi on on how lea ding ca dres of party members "two" curre nt, "two" activity is in full swing up a nd dow n the country, party cadre s a s a "key minority" is bot h a barometer and impetus. The "two" meani ng enoug h dee p, is to determine t he party ca dres can res olve to study har d first. In the "tw o" in the pr oce ss, s ome ca dres of himse lf, standing l ong, high awar enes s, that Constitution Party rule s is simpl e, its not worth bothering s ome party ca dres thi nk s pea k series ha s not hing to do wit h the grass -roots work , water busine ss lear ning seri es of s peeches s een a s window dressi ng. These "lazy, cas ual, a nd deca dent" idea s learni ng lacks m otivation, a serious impe diment to "two" effect. John Stuart M ill once sa id, only a ba sic el ement of human thoug ht patterns change dramaticall y, human de stiny ca n make great improvement. T he same, only party members

and

Learn G eneral Se cretary on "two to learn a" stre ngthe ning "four Consci ousnes ses" important speech ca use d a strong reaction in t he country. T ime, watching "red treas ure", the origi n of buildi ng the party back t o power, how t o strengthen s ervice s for the masse s, improve party cohesi on, fighting to become t he grass -roots party members a nd ma sses hot topic. Grass -root s party organizations "two" is to stre ngthe n the s ervice of party members a nd ca dres, t he pi one er spirit. Distribution of grass -root s party orga nizations in a ll walks of people, cl othi ng, s helter, w hi ch belongs to the nerve endi ngs of th e party organization and comme nts reputation has a direct perce ption of the mass es. Strengthen the party ahea d of the "pe dal" s pirit; strengt hen t he party members and cadre s "succes s does not have to be me" and "the first to bear hards hips , the last to" s ervice spirit to set the party's positive image am ong the pe ople i s importa nt. Grass -roots party organizati ons "two" is t o clea nse all people not ha ppy not to se e "stereotype s", establi sh the honest faithful, diligent faith for t he pe opl e. No nee d to avoi d menti oni ng that, s ome members of our party can not sta nd the "money," corrosion of temptation, thi n, Xu Zhou, s uch abuse a nd corr upt br iber y, malfeasance borers, a nd rats. Two, is to clean up, t hin, Xu, Z hou's s oluti on to rest ore the party's fresh a nd natural, s olid a nd honest w ork style. Cleansing "take, eat, card," undesirabl e and be haviour, "cr oss, hard a nd col d, push" attitude. Gras s-r oots party organizati ons "two" is to stre ngthe n the se nse of ordi nary party members, parti cipating i n consci ous nes s, unity cons ciousness. F or reasons k now n, members of grass-r oots party branche s less m obil e, less re sources , and the constructi on of party organi zations have some lag. Tw o studies, i s to focus on the grass-r oots party branche s "loose, s oft, loose" problem , advance the party members and ca dres, "a gang w orking", "Hong Kong re port." Strong cleanup a ctions, style and rambli ng, pre sumpt uous "unqualifie d" party members, pay s special attenti on to party members a nd ca dres "joi ning party of thought" problem. "Party buildi ng" is obtai ned i n the l ong -term development of our party's histori cal experi ence accumul ated. Two i s our party under the new histori cal conditions, stre ngthe n the party's constr uction of a ne w "rectification movement." Gras s-r oots party organizati ons shoul d always cat ch the hard w ork, res ults-oriente d. Two educational outcome s are long -term orie nted and become a n important impetus for the w ork. "Two" shoul d have thre e kinds of consci ousne ss "two" study and education, ba sic lear ning lie s in the doi ng. Only the Constituti on address t he serie s of party rule s, and do soli d work, be qualified party members ha d a s olid ideol ogical basis . Only the "learni ng" and "do" real unit y, to form a "learn-l earn-do-do" the virtuous cycle, and ultimately achieve the fundamental obje ctive of education. T his requires that t he Organization

分析:本题中的函数 f ?x ?, g ?x ? 由列表法进行表示,只需将 x 进行逐个验证即可. 解:∵ g ?1? ? 3 ,∴ f ? ? g ?1? ? ? ? f ? 3? ? 1 ; 当 x ? 1 时, f ? ? g ?1? ? ? ? f ? 3? ? 1 , g ? ? f ?1? ? ? ? g ?1? ? 3 ; 当 x ? 2 时, f ? ? g ? 2 ?? ? ? f ? 2? ? 3 , g ? ? f ? 2 ?? ? ? g ? 3? ? 1 ; 当 x ? 3 时, f ? ? g ? 3? ? ? ? f ?1? ? 1 , g ? ? f ? 3? ? ? ? g ?1? ? 3 . 所以 x ? 2 . 归纳小结: (1)本题考查了函数概念、表达形式、函数值等知识,考查了转化、化归思 想和分析问题和解决问题的能力. (2)函数表达形式有解析式法、图象法和列表法.其中列表法就是列出表格来表示两 个变量的函数关系. 其优点是不需要计算就可以直接看出与自变量的值相对应的函数值. 因 此在解决本题时只需把 x 的值逐个代入验证即可. 例 9( 2008 江西卷)若函数 y ? f ( x) 的值域是 [ , 3] ,则函数 F ( x) ? f ( x) ? 值域是( ) B. [2,

1 2

1 的 f ( x)

1 A. [ , 3] 2

10 ] 3

C. [ ,

5 10 ] 2 3

D. [3,

10 ] 3

解:∵ f ? x ? ? 0 , ∴ F ( x) ? f ( x) ? 当 f ? x? ?

1 ? 2 .当且仅当 f ? x ? ? 2 时,取等号. f ( x)

1 5 时, F ( x) ? ; 2 2 10 当 f ? x ? ? 3 时, F ? x ? ? . 3 10 所以 F ? x ? 的值域为 [2, ] ,选 B. 3
归纳小结:(1)本题考查了函数的值域、 均值不等式等基本知识, 还考查了函数与不等式 的转化与整合的数学思想和计算、推理能力. (2)求函数值域的方法比较多,常见的主要有: ①直接法;②反函数法;③配方法;④分离常数法;⑤不等式法;⑥换元法;⑦判别式 法;⑧数形结合法;⑨导数法等. 本题从函数形式及 f ? x ? 的值域可以判断出使用不等式法确定 F ? x ? 的最小值,再比较 连续函数 F ? x ? 在闭区间上的端点值中的较大值,从而判断出所求值域.

learning e ducation, nee d three ki nds of consciousne ss: one i s to establi sh a n integrated aware nes s. "Lear ning" and "do" what car isTwo -w heel, bird wi ngs, need to g o ha nd in hand, one e nd ca n be negle cted. Communist the oreticia n and man. Only by clos ely com bini ng the ory and practi ce togethe r in order to tr uly realize the ir value. "Le arni ng" is the Foundati on, t he Foundati on i s not str ong, s haki ng; " "Is the key to net to net thousa nds of accounts. 。 泄 宣 值 价 感 情 华 升 结 总 验 经 识 知 活 实 炼 提 头 口 言 语 用 运 句 词 字 对 于 在 现 表 更 性 要 重 它 , 忆 记 和 考 思 象 想 联 、 力 察 观 的 生 学 养 培 能 但 不 作 写

"Two" education, "" lay the basi s, goi ng to "do" the key grip, so that t he "learni ng" and "doing" ba ck to standard, so that t he majority of party members "learn" learni ng the ory of nutrie nts, i n the "doing" practi ce party's pur poses. Se cond, to e stablis h a se nse of dept h. "Lear ning" and "do" not Chu drawn, entirely different, but the organi c unity of the whole. "Two" lear ning educati on, we nee d to expl ore integrating "lear ning" in "do", exhibit "do" in "Scie nce". To avoi d the "learni ng" into sim ple room i nstruction, "do" int o a monotone for

doing . Should expl oration "learn" in the has "do", "do" in the has "learn" of e ducati on a nd practice of carrie r, makes general gras s-roots members can i n "learn" in the has "do" of achi evements s ens e, in "do" in the ha s "learn" of get sense, real makes party of theory brai n into heart, put for people servi ce concept outsi de of Yu s hape d. T hird, to a dhere to long-term the aw arenes s. Style constr ucti on on the r oad forever, "two" had to catch t he long-term. "Two" study and educati on, by no mea ns, as sault -style wind-sport, but the recurrent e ducation withi n the part y. In re cent year s, the party's mass line education pra ctice a nd "three -thre e" spe cial educati on i n grass-r oots bor ne rich fruits, vast numbers of party members and ca dres withstood the bapti sm of the spirit . "Two" greater need to focus on l onger hol d long-term, to esta blis h and perfect the effective mecha nism of the education, focusing on the creation of long-term educati on, strive to make the vast num ber of party members t o maintain their va nguard Col or, maintai n the party's adva nce d nature a nd purit y. Awarene ss -raising , antennas a nd atmosp here – a di scussi on on how lea ding ca dres of party members "two" curre nt, "two" activity is in full swing up a nd dow n the country, party cadre s as a "key minority" is bot h a barometer and impetus. The "two" meani ng enoug h dee p, is to determine t he party ca dres can res olve to study har d first. In the "tw o" in the pr oce ss, s ome ca dres of himse lf, standing l ong, high awar enes s, that Constitution Party rule s is simpl e, its not worth bothering s ome party ca dres thi nk s pea k series ha s not hing to do wit h the grass -roots work , water busine ss lear ning seri es of s peeches s een a s window dressi ng. These "lazy, cas ual, a nd deca dent" idea s learni ng lacks m otivation, a serious impe diment to "two" effect. John Stuart M ill once sa id, only a ba sic el ement of human thoug ht patterns change dramaticall y, human de stiny ca n make great improvement. T he same, only party members

and

7

Learn G eneral Se cretary on "two to learn a" stre ngthe ning "four Consci ousnes ses" important speech ca use d a strong reaction in t he cou ntry. T ime, watching "red treas ure", the origi n of buildi ng the party back t o power, how t o strengthen s ervice s for the masse s, improve party cohesi on, fighting to become t he grass -roots party members a nd ma sses hot topic. Grass -root s party organizations "two" is to stre ngthe n the s ervice of party members a nd ca dres, t he pi one er spirit. Distribution of grass -root s party orga nizatio ns in a ll walks of people, cl othi ng, s helter, w hi ch belongs to the nerve endi ngs of the party organization and comme nts reput ation has a direct perce ption of the mass es. Strengthen the party ahea d of the "pe dal" s pirit; strengt hen t he party members and cadre s "succes s does not have to be me" and "the first to bear hards hips , the last to" s ervice spirit to set the party's posi tive image am ong the pe ople i s importa nt. Grass -roots party organizati ons "two" is t o clea nse all people not ha ppy not to se e "stereotype s", establi sh the honest faithful, diligent faith for t he pe opl e. No nee d to avoi d menti oni ng that, s ome members of our party can not sta nd the "money," corrosion of temptation, thi n, Xu Zhou, s uch abuse a nd corr upt br iber y, malfeasance borers, a nd rats. Two, is to clean up, t hin, Xu, Z hou's s oluti on to rest ore the party's fresh a nd natural, s olid a nd honest w ork style. Cleansing "take, eat, card," undesirabl e and be haviour, "cr oss, hard a nd col d, push" attitude. Gras s-r oots party organizati ons "two" is to stre ngthe n the se nse of ordi nary party members, parti cipating i n consci ous nes s, unity cons ciousness. F or reasons k now n, members of grass-r oots party branche s less m obil e, less re sources , and the constructi on of party organi zations have some lag. Tw o studies, i s to focus on the grass-r oots party branche s "loose, s oft, loose" problem, advance the party members and ca dres, "a gang w orking", "Hong Kong re port." Strong cleanup a ctions, style and rambli ng, pre sumpt uous "unqualifie d" party members, pay s special attenti on to party members a nd ca dres "joi ning party of thought" problem. "Party buildi ng" is obtai ned i n the l ong -term development of our party's histori cal experi ence accumul ated. Two i s our party under the new histori cal conditions, stre ngthe n the party's constr uction of a ne w "rectification movement." Gras s-r oots party organizati ons shoul d always cat ch the hard w ork, res ults-oriente d. Two educational outcome s are long -term orie nted and become a n important impetus for the w ork. "Two" shoul d have thre e kinds of consci ousne ss "two" study and education, ba sic lear ning lie s in the doi ng. Only the Constituti on address t he serie s of party rule s, and do soli d work, be qualified party members ha d a s olid ideol ogical basis . Only the "learni ng" and "do" real unit y, to form a "learn-l earn-do-do" the virtuous cycle, and ultimately achieve the fundamental obje ctive of education. T his requires that t he Organization

例 10( 2007 浙江卷)设 f ? x ? ? ? 是 ?0,??? ,则 g ?x ? 的值域是( A. ?? ?,?1? ? ? 1,???

?x 2 , ? x,


x ?1 , g ?x ? 是二次函数,若 f ?g ?x ?? 的值域 x ?1

B. ?? ?,?1? ? ?0,???

C. ?0,???

D. ?1,???

解:由函数 f ? x ? 解析式可知当 x ? ? ??, ?1? 值域是 ?0,??? 时, g ? x ? ? ? ??, ?1? C.

?0, ??? 时, f ? x? ? 0 ,所以 f ?g ?x?? 的

?0, ??? .因为 g ? x ? 是二次函数,结合选项,判断选

归纳小结: (1)本题考查了复合函数的值域与分段函数、二次函数的知识,考查了二 次函数的图象与值域的判断方法,考查了数形结合思想. (2)本题在求解过程中要注意结合选项合理地进行取舍. (3)求函数值域没有固定的方法和解题模式,要熟悉几种常见的求值域的方法,在问 题解决过程中选择最优解法. 例 11 ( 2009 年 海 南 卷 ) 用 m i n , c,? 表 示 a, b, c 三 个 数 中 的 最 小 值 . 设 ?a b
x f ? x? ? m i n ,x? 2 , 1 ?0? x? x ? ? ,则 0 f ? x ? 的最大值为( ?2



A.4

B.5

C.6

D.7

分析:利用作差法比较难以解决本题,因此可以结合图象解决问题.
x 解:画出 y ? 2 , y ? x ? 2 , y ? 10 ? x 的图象,如右图,观察图象可知,当 0 ? x ? 2

x 时, f ? x ? ? 2 ,当 2 ? x ? 3 时, f ? x ? ? x ? 2 ,当 x ? 4 时, f ? x ? ? 10 ? x .所以 f ? x ?

的最大值在 x ? 4 时取得为 6 ,故选 C.

归纳小结: (1)本题主要考查了初等函数的图象与函数值的大小比较,考查数形结合思 想和转化思想,考查了识图和用图的能力和知识迁移能力. (2)利用图象解决函数的最大值和最小值是一种常见的考题形式,要熟记几种基本函 数的图象与性质. (3)本题是有一定创新意义的问题,抓住问题的定义,转化为绘制 f ? x ? 的图象成为
learning e ducation, nee d three ki nds of consciousne ss: one i s to establi sh a n integrated aware nes s. "Lear ning" and "do" what car isTwo -w heel, bird wi ngs, need to g o ha nd in hand, one e nd ca n be negle cted. Communist the oreticia n and man. Only by clos ely com bini ng the ory and practi ce togethe r in order to tr uly realize the ir value. "Le arni ng" is the Foundati on, t he Foundati on i s not str ong, s haki ng; " "Is the key to net to net thousa nds of accounts. 。 泄 宣 值 价 感 情 华 升 结 总 验 经 识 知 活 实 炼 提 头 口 言 语 用 运 句 词 字 对 于 在 现 表 更 性 要 重 它 , 忆 记 和 考 思 象 想 联 、 力 察 观 的 生 学 养 培 能 但 不 作 写 "Two" education, "" lay the basi s, goi ng to "do" the key grip, so that t he "learni ng" and "doing" ba ck to standard, so that t he majority of party members "learn" learni ng the ory of nutrie nts, i n the "doing" practi ce party's pur poses. Se cond, to e stablis h a se nse of dept h. " Lear ning" and "do" not Chu drawn, entirely different, but the organi c unity of the whole. "Two" lear ning educati on, we nee d t o expl ore integrating "lear ning" in "do", exhibit "do" in "Scie nce". To avoi d the "learni ng" into sim ple room i nstruction, "do" int o a monotone for doing . Should expl oration "learn" in the has "do", "do" in the has "learn" of e ducati on a nd practice of carrie r, makes general gras s-roots members can i n "learn" in the has "do" of achi evements s ens e, in "do" in the ha s "learn" of get sense, real makes party of theory brai n into heart, put for people servi ce concept outsi de of Yu s hape d. T hird, to a dhere to long-term the aw arenes s. Style constr ucti on on the r oad forever, "two" had to catch t he long-term. "Two" study and educati on, by no mea ns, as sault -style wind-sport, but the recurrent e ducation withi n the part y. In re cent year s, the party's mass line education pra ctice a nd "three -thre e" spe cial educati on i n grass-r oots bor ne rich fruits, vast numbers of party members and ca dres withstood the bapti sm of the spirit . "Two" greater need to focus on l onger hol d long-term, to esta blis h and perfect the effective mecha nism of the education, focusing on the creation of long-term educati on, strive to make the vast num ber of party members t o maintain their va nguard Col or, maintai n the party's adva nce d nature a nd purit y. Awarene ss -raising , antennas a nd atmosphere – a di scussi on on how lea ding ca dres of party members "two" curre nt, "two" activity is in full swing up a nd dow n the country, party cadre s a s a "key minority" is bot h a barometer and impetus. The "two" meani ng enoug h dee p, is to determine t he party ca dres can res olve to study har d first. In the "tw o" in the pr oce ss, s ome ca dres of himse lf, standing l ong, high awar enes s, that Constitution Party rule s is simpl e, its not worth bothering s ome party ca dres thi nk s pea k series ha s not hing to do wit h the grass -roots work , water busine ss lear ning seri es of s peeches s een a s window dressi ng. These "lazy, cas ual, a nd deca dent" idea s learni ng lacks m otivation, a serious impe diment to "two" effect. John Stuart M ill once sa id, only a ba sic el ement of human thoug ht patterns change dramaticall y, human de stiny ca n make great improvement. T he same, only party members

and

8

Learn G eneral Se cretary on "two to learn a" stre ngthe ning "four Consci ousnes ses" important speech ca use d a strong reaction in t he country. T ime, watching "red treas ure", the origi n of buildi ng the party back t o power, how t o strengthen s ervice s for the masse s, improve party cohesi on, fighting to become t he grass -roots party members a nd ma sses hot topic. Grass -root s party organizations "two" is to stre ngthe n the s ervice of party members a nd ca dres, t he pi one er spirit. Distribution of grass -root s party orga nizations in a ll walks of people, cl othi ng, s helter, w hi ch belongs to the nerve endi ngs of th e party organization and comme nts reputation has a direct perce ption of the mass es. Strengthen the party ahea d of the "pe dal" s pirit; strengt hen t he party members and cadre s "succes s does not have to be me" and "the first to bear hards hips , the last to" s ervice spirit to set the party's positive image am ong the pe ople i s importa nt. Grass -roots party organizati ons "two" is t o clea nse all people not ha ppy not to se e "stereotype s", establi sh the honest faithful, diligent faith for t he pe opl e. No nee d to avoi d menti oni ng that, s ome members of our party can not sta nd the "money," corrosion of temptation, thi n, Xu Zhou, s uch abuse a nd corr upt br iber y, malfeasance borers, a nd rats. Two, is to clean up, t hin, Xu, Z hou's s oluti on to rest ore the party's fresh a nd natural, s olid a nd honest w ork style. Cleansing "take, eat, card," undesirabl e and be haviour, "cr oss, hard a nd col d, push" attitude. Gras s-r oots party organizati ons "two" is to stre ngthe n the se nse of ordi nary party members, parti cipating i n consci ous nes s, unity cons ciousness. F or reasons k now n, members of grass-r oots party branche s less m obil e, less re sources , and the constructi on of party organi zations have some lag. Tw o studies, i s to focus on the grass-r oots party branche s "loose, s oft, loose" problem , advance the party members and ca dres, "a gang w orking", "Hong Kong re port." Strong cleanup a ctions, style and rambli ng, pre sumpt uous "unqualifie d" party members, pay s special attenti on to party members a nd ca dres "joi ning party of thought" problem. "Party buildi ng" is obtai ned i n the l ong -term development of our party's histori cal experi ence accumul ated. Two i s our party under the new histori cal conditions, stre ngthe n the party's constr uction of a ne w "rectification movement." Gras s-r oots party organizati ons shoul d always cat ch the hard w ork, res ults-oriente d. Two educational outcome s are long -term orie nted and become a n important impetus for the w ork. "Two" shoul d have thre e kinds of consci ousne ss "two" study and education, ba sic lear ning lie s in the doi ng. Only the Constituti on address t he serie s of party rule s, and do soli d work, be qualified party members ha d a s olid ideol ogical basis . Only the "learni ng" and "do" real unit y, to form a "learn-l earn-do-do" the virtuous cycle, and ultimately achieve the fundamental obje ctive of education. T his requires that t he Organization

解题关键.

?1 ? f ? n ? , n为偶数, 例 12 定义在 N 上的函数 f ? x ? 满足 f ?1? ? 1,且 f ? n ? 1? ? ? 2 ? f ? n ? , n为奇数, ?
*

则 f ? 22? ? ______ . 分析:本题考查了抽象分段函数求函数值的问题.如果直接求解,则未知条件较多,因 此从题目条件入手,对 n 分类讨论,找到 f ? n ? 与 f ? n ? 1? 的关系成为解题关键.

解:由

?1 ? f ? n ? , n为偶数, f ? n ? 1? ? ? 2 得: ? f ? n ? , n为奇数, ?
f ? n ? 1? 1 ? ; f ? n? 2

当 n 为偶数时,

当 n 为奇数时, f ? n ?1? ? f ? n? . 所以 f ? 22 ? ? f ? 21? ?

f ? 21? f ? 20? f ? 3? f ? 2 ? ? ??? ? ? f ?1? f ? 20? f ?19? f ? 2? f ?1?
10

f ? 21? f ?19 ? f ? 3? ? 1 ? 1 ? ? ??? ?? ? ? . f ? 20 ? f ?18 ? f ? 2? ? 2 ? 1024
归纳小结: (1)本题考查了求分段函数和抽象函数的函数的知识和方法,考查了数形结 合思想,以及根据条件分析问题、灵活解题的能力. (2)对于抽象函数的问题的解决,要根据问题和条件灵活地进行变形,合理地推理分 析是关键.

四、本专题总结
1.要深化对函数概念的理解,从函数三要素(定义域、值域与对应法则)整体上去把 握函数概念.在函数三要素中,定义域是灵魂,对应法则是函数的核心,因值域可由定义域 和对应法则确定, 所以两个函数当且仅当二者均相同时才表示同一个函数, 而值域相同是两 函数为同一函数的必要非充分条件. 2.求函数解析式的方法主要有:待定系数法、换元法、配方法、函数方程法、赋值法 等. 已知函数为某类基本初等函数时用待定系数法, 已知复合函数的问题时用换元法或配方 法,抽象型函数问题一般用赋值法或函数方程法. 3.求函数定义域的常见题型及求法: (1)已知函数的解析式求其定义域,只要使解析式有意义即可. (2) 已知 f ? 求 f ? x ? 的定义域, 实质上求 g ? x ? 在 A 上的值域; ? g ? x ?? ? 的定义域为 A , 已知函数 f ? x ? 的定义域为 A ,求函数 f ? ? g ? x ?? ? 的定义域,实质上使 g ? x ? ? A ,解不等

learning e ducation, nee d three ki nds of consciousne ss: one i s to establi sh a n integrated aware nes s. "Lear ning" and "do" what car isTwo -w heel, bird wi ngs, need to g o ha nd in hand, one e nd ca n be negle cted. Communist the oreticia n and man. Only by clos ely com bini ng the ory and practi ce togethe r in order to tr uly realize the ir value. "Le arni ng" is the Foundati on, t he Foundati on i s not str ong, s haki ng; " "Is the key to net to net thousa nds of accounts. 。 泄 宣 值 价 感 情 华 升 结 总 验 经 识 知 活 实 炼 提 头 口 言 语 用 运 句 词 字 对 于 在 现 表 更 性 要 重 它 , 忆 记 和 考 思 象 想 联 、 力 察 观 的 生 学 养 培 能 但 不 作 写

"Two" education, "" lay the basi s, goi ng to "do" the key grip, so that t he "learni ng" and "doing" ba ck to standard, so that t he majority of party members "learn" learni ng the ory of nutrie nts, i n the "doing" practi ce party's pur poses. Se cond, to e stablis h a se nse of dept h. "Lear ning" and "do" not Chu drawn, entirely different, but the organi c unity of the whole. "Two" lear ning educati on, we nee d to expl ore integrating "lear ning" in "do", exhibit "do" in "Scie nce". To avoi d the "learni ng" into sim ple room i nstruction, "do" int o a monotone for

doing . Should expl oration "learn" in the has "do", "do" in the has "learn" of e ducati on a nd practice of carrie r, makes general gras s-roots members can i n "learn" in the has "do" of achi evements s ens e, in "do" in the ha s "learn" of get sense, real makes party of theory brai n into heart, put for people servi ce concept outsi de of Yu s hape d. T hird, to a dhere to long-term the aw arenes s. Style constr ucti on on the r oad forever, "two" had to catch t he long-term. "Two" study and educati on, by no mea ns, as sault -style wind-sport, but the recurrent e ducation withi n the part y. In re cent year s, the party's mass line education pra ctice a nd "three -thre e" spe cial educati on i n grass-r oots bor ne rich fruits, vast numbers of party members and ca dres withstood the bapti sm of the spirit . "Two" greater need to focus on l onger hol d long-term, to esta blis h and perfect the effective mecha nism of the education, focusing on the creation of long-term educati on, strive to make the vast num ber of party members t o maintain their va nguard Col or, maintai n the party's adva nce d nature a nd purit y. Awarene ss -raising , antennas a nd atmosp here – a di scussi on on how lea ding ca dres of party members "two" curre nt, "two" activity is in full swing up a nd dow n the country, party cadre s as a "key minority" is bot h a barometer and impetus. The "two" meani ng enoug h dee p, is to determine t he party ca dres can res olve to study har d first. In the "tw o" in the pr oce ss, s ome ca dres of himse lf, standing l ong, high awar enes s, that Constitution Party rule s is simpl e, its not worth bothering s ome party ca dres thi nk s pea k series ha s not hing to do wit h the grass -roots work , water busine ss lear ning seri es of s peeches s een a s window dressi ng. These "lazy, cas ual, a nd deca dent" idea s learni ng lacks m otivation, a serious impe diment to "two" effect. John Stuart M ill once sa id, only a ba sic el ement of human thoug ht patterns change dramaticall y, human de stiny ca n make great improvement. T he same, only party members

and

9

Learn G eneral Se cretary on "two to learn a" stre ngthe ning "four Consci ousnes ses" important speech ca use d a strong reaction in t he cou ntry. T ime, watching "red treas ure", the origi n of buildi ng the party back t o power, how t o strengthen s ervice s for the masse s, improve party cohesi on, fighting to become t he grass -roots party members a nd ma sses hot topic. Grass -root s party organizations "two" is to stre ngthe n the s ervice of party members a nd ca dres, t he pi one er spirit. Distribution of grass -root s party orga nizatio ns in a ll walks of people, cl othi ng, s helter, w hi ch belongs to the nerve endi ngs of the party organization and comme nts reput ation has a direct perce ption of the mass es. Strengthen the party ahea d of the "pe dal" s pirit; strengt hen t he party members and cadre s "succes s does not have to be me" and "the first to bear hards hips , the last to" s ervice spirit to set the party's posi tive image am ong the pe ople i s importa nt. Grass -roots party organizati ons "two" is t o clea nse all people not ha ppy not to se e "stereotype s", establi sh the honest faithful, diligent faith for t he pe opl e. No nee d to avoi d menti oni ng that, s ome members of our party can not sta nd the "money," corrosion of temptation, thi n, Xu Zhou, s uch abuse a nd corr upt br iber y, malfeasance borers, a nd rats. Two, is to clean up, t hin, Xu, Z hou's s oluti on to rest ore the party's fresh a nd natural, s olid a nd honest w ork style. Cleansing "take, eat, card," undesirabl e and be haviour, "cr oss, hard a nd col d, push" attitude. Gras s-r oots party organizati ons "two" is to stre ngthe n the se nse of ordi nary party members, parti cipating i n consci ous nes s, unity cons ciousness. F or reasons k now n, members of grass-r oots party branche s less m obil e, less re sources , and the constructi on of party organi zations have some lag. Tw o studies, i s to focus on the grass-r oots party branche s "loose, s oft, loose" problem, advance the party members and ca dres, "a gang w orking", "Hong Kong re port." Strong cleanup a ctions, style and rambli ng, pre sumpt uous "unqualifie d" party members, pay s special attenti on to party members a nd ca dres "joi ning party of thought" problem. "Party buildi ng" is obtai ned i n the l ong -term development of our party's histori cal experi ence accumul ated. Two i s our party under the new histori cal conditions, stre ngthe n the party's constr uction of a ne w "rectification movement." Gras s-r oots party organizati ons shoul d always cat ch the hard w ork, res ults-oriente d. Two educational outcome s are long -term orie nted and become a n important impetus for the w ork. "Two" shoul d have thre e kinds of consci ousne ss "two" study and education, ba sic lear ning lie s in the doi ng. Only the Constituti on address t he serie s of party rule s, and do soli d work, be qualified party members ha d a s olid ideol ogical basis . Only the "learni ng" and "do" real unit y, to form a "learn-l earn-do-do" the virtuous cycle, and ultimately achieve the fundamental obje ctive of education. T his requires that t he Organization

式即可. (3)涉及实际问题的定义域问题必须考虑问题的实际意义. (4)当解析式中含有参数时,需对参数进行讨论. 4.定义域问题经常作为基本条件出现在试题中,具有一定的隐蔽性.所以在解决函数 问题时,必须树立起“定义域优先”的观点.

learning e ducation, nee d three ki nds of consciousne ss: one i s to establi sh a n integrated aware nes s. "Lear ning" and "do" what car isTwo -w heel, bird wi ngs, need to g o ha nd in hand, one e nd ca n be negle cted. Communist the oreticia n and man. Only by clos ely com bini ng the ory and practi ce togethe r in order to tr uly realize the ir value. "Le arni ng" is the Foundati on, t he Foundati on i s not str ong, s haki ng; " "Is the key to net to net thousa nds of accounts. 。 泄 宣 值 价 感 情 华 升 结 总 验 经 识 知 活 实 炼 提 头 口 言 语 用 运 句 词 字 对 于 在 现 表 更 性 要 重 它 , 忆 记 和 考 思 象 想 联 、 力 察 观 的 生 学 养 培 能 但 不 作 写

"Two" education, "" lay the basi s, goi ng to "do" the key grip, so that t he "learni ng" and "doing" ba ck to standard, so that t he majority of party members "learn" learni ng the ory of nutrie nts, i n the "doing" practi ce party's pur poses. Se cond, to e stablis h a se nse of dept h. " Lear ning" and "do" not Chu drawn, entirely different, but the organi c unity of the whole. "Two" lear ning educati on, we nee d t o expl ore integrating "lear ning" in "do", exhibit "do" in "Scie nce". To avoi d the "learni ng" into sim ple room i nstruction, "do" int o a monotone for

doing . Should expl oration "learn" in the has "do", "do" in the has "learn" of e ducati on a nd practice of carrie r, makes general gras s-roots members can i n "learn" in the has "do" of achi evements s ens e, in "do" in the ha s "learn" of get sense, real makes party of theory brai n into heart, put for people servi ce concept outsi de of Yu s hape d. T hird, to a dhere to long-term the aw arenes s. Style constr ucti on on the r oad forever, "two" had to catch t he long-term. "Two" study and educati on, by no mea ns, as sault -style wind-sport, but the recurrent e ducation withi n the part y. In re cent year s, the party's mass line education pra ctice a nd "three -thre e" spe cial educati on i n grass-r oots bor ne rich fruits, vast numbers of party members and ca dres withstood the bapti sm of the spirit . "Two" greater need to focus on l onger hol d long-term, to esta blis h and perfect the effective mecha nism of the education, focusing on the creation of long-term educati on, strive to make the vast num ber of party members t o maintain their va nguard Col or, maintai n the party's adva nce d nature a nd purit y. Awarene ss -raising , antennas a nd atmosphere – a di scussi on on how lea ding ca dres of party members "two" curre nt, "two" activity is in full swing up a nd dow n the country, party cadre s a s a "key minority" is bot h a barometer and impetus. The "two" meani ng enoug h dee p, is to determine t he party ca dres can res olve to study har d first. In the "tw o" in the pr oce ss, s ome ca dres of himse lf, standing l ong, high awar enes s, that Constitution Party rule s is simpl e, its not worth bothering s ome party ca dres thi nk s pea k series ha s not hing to do wit h the grass -roots work , water busine ss lear ning seri es of s peeches s een a s window dressi ng. These "lazy, cas ual, a nd deca dent" idea s learni ng lacks m otivation, a serious impe diment to "two" effect. John Stuart M ill once sa id, only a ba sic el ement of human thoug ht patterns change dramaticall y, human de stiny ca n make great improvement. T he same, only party members

and

10


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