高一必修一数学函数的定义域、值域专题训练(打印版)

Pushing ahead, East, North, West development, facilitating shanty, complete xincheng West Road, stability and reconstruction of the street, Star Ding garden built century Garden District, subject public housing construction, heating the gas expansion accelerated implementation, Jing Rui River and bridge style line solid shaft, further expanded the town development. Beautiful country adhere to the advance and typical for a group to lead. According to \ogical lay based, and industry increased income, and live upgrade civilization, and culture rich connotation\ht, caught built beautiful village, and whole village advance, and easily relocation, and \d three built\oject near 30 a; depth into ecological, and industry, and culture, and tourism, elements, high standards caught party original city Liu, and jade are Xia AO, model village, in province City set has benchmark. Four is equal benefits to promote sharing, coordinated development of various social undertakings. In the case of rigid spending slowing revenue growth, increase, financial 75% to the people's livelihood, the masses have more access in the sharing. Cuoban something good and benefit. Adhere to the affordable, best, carefully cuoban village oil, water and heat, cultural, city and County columns practical, developments benefit families, bring more welfare to the masses. Development of social convenience. Acceptance of balanced development of compulsory education through the national assessment, the County vocational education center was named \chool of vocational education in China\hird batch of national reform and development model through provincial ... Five is to deepen reform and innovation to break bottlenecks and endogenous development of effective fire. As an engine of dynamism, adding reform key to adopting reform measures stress energy and break bottlenecks and promoting development. Pay close attention to the key areas of reform. Conscientiously implement the provincial deployment and cancel, adjustment, to undertake the administrative approval items according to Regulation 347 to further improve administrative efficiency continuing deepening reform for poverty alleviation, speeding up rural land right registration certification pilot project, encouraging the orderly transfer of land management, utilize the land resources, in order to promote scale management laid the Foundation. Actively cultivate the market. Firmly establish a market-oriented, nurturing family farms, industrial users, professional cooperation organization new market management main body 456, effectively improve the industry, intensive and marketization of encouraging support social capital into the small micro-credit, urban development, culture and tourism, public services and other areas, easing development shortfall. To promote mass innovation. o support the rural sector to use new thinking and new ideas, creative work incentives such as actively promoting financial intermediation, bring added 159 in non public enterprises, individually-1540, created a函数定义域、值域专题教案与练习

一、函数的定义域 1．函数定义域的求解方法

求函数的定义域主要是通过解不等式（组）或方程来获得．一般地，我们约定：如果不加说明，所谓函数的定义域就是自变量使函数解析式有意义的实数的集合． （1）若f(x)是整式，则定义域为全体实数．

（2）若f(x)是分式，则定义域为使分母不为零的全体实数． （3）若f(x)是偶次根式，则定义域为使被开方式为非负的全体实数． （4）若f(x)为对数式，则定义域为真数大于零的全体实数。

（5）若f(x)为复合函数，则定义域由复合的各基本的定义域所组成的不等式组确定．如：f(x)的定义域为[a,b]，则复合函数f[g(x)]的定义域应由不等式a?g(x)?b解出． （5）由实际问题确定的函数，其定义域由自变量的实际意义确定． 2．求函数定义域的常见问题：

（1）若已知函数解析式比较复杂，求定义域时通常根据各种条件列不等式组求解；

（2）由y?f(x)的定义域，求复合函数f[g(x)]的问题，实际上是已知中间变量u?g(x)的值域，求自变量x的取值范围问题；

（3）对含有字母参数的函数，求其定义域时注意对字母参数的一切允许值分类讨论； （4）若是实际问题除应考虑解析式有意义外，还应使实际问题有意义． 二、求函数的值域常用方法

（1）观察法：通过对函数解析式的简单变形，利用熟知的基本函数值域求解； （2）单调性法：利用函数的单调性求解

（3）换元法：通过对函数解析式进行适当换元，可以将复杂的函数化归为几个简单的函数，从而利用基本函数的取值范围求函数的值域。

三、初等函数：指数函数、对数函数、幂函数的定义域、值域

1.指数函数：f(x)?a(a?0,a?1)，定义域：x?R；值域：f(x)?(0,??)； 2.对数函数：f(x)?logax(a?0,a?1)，定义域：x?(0,??)；值域：f(x)?R

3.幂函数：f(x)?x（??R)，其定义域、值域随?的取值而不同，但在x?(0,??)都有意义。

四、例题分析

x?Pushing ahead, East, North, West development, facilitating shanty, complete xincheng West Road, stability and reconstruction of the street, Star Ding garden built century Garden District, subject public housing construction, heating the gas expansion accelerated implementation, Jing Rui River and bridge style line solid shaft, further expanded the town development. Beautiful country adhere to the advance and typical for a group to lead. According to \ogical lay based, and industry increased income, and live upgrade civilization, and culture rich connotation\ht, caught built beautiful village, and whole village advance, and easily relocation, and \d three built\oject near 30 a; depth into ecological, and industry, and culture, and tourism, elements, high standards caught party original city Liu, and jade are Xia AO, model village, in province City set has benchmark. Four is equal benefits to promote sharing, coordinated development of various social undertakings. In the case of rigid spending slowing revenue growth, increase, financial 75% to the people's livelihood, the masses have more access in the sharing. Cuoban something good and benefit. Adhere to the affordable, best, carefully cuoban village oil, water and heat, cultural, city and County columns practical, developments benefit families, bring more welfare to the masses. Development of social convenience. Acceptance of balanced development of compulsory education through the national assessment, the County vocational education center was named \chool of vocational education in China\hird batch of national reform and development model through provincial ... Five is to deepen reform and innovation to break bottlenecks and endogenous development of effective fire. As an engine of dynamism, adding reform key to adopting reform measures stress energy and break bottlenecks and promoting development. Pay close attention to the key areas of reform. Conscientiously implement the provincial deployment and cancel, adjustment, to undertake the administrative approval items according to Regulation 347 to further improve administrative efficiency continuing deepening reform for poverty alleviation, speeding up rural land right registration certification pilot project, encouraging the orderly transfer of land management, utilize the land resources, in order to promote scale management laid the Foundation. Actively cultivate the market. Firmly establish a market-oriented, nurturing family farms, industrial users, professional cooperation organization new market management main body 456, effectively improve the industry, intensive and marketization of encouraging support social capital into the small micro-credit, urban development, culture and tourism, public services and other areas, easing development shortfall. To promote mass innovation. o support the rural sector to use new thinking and new ideas, creative work incentives such as actively promoting financial intermediation, bring added 159 in non public enterprises, individually-1540, created a例1：求函数f(x)?

2x?1?12?x?1的定义域。 x例2：求函数f(x)?ln(x?1)?lg(x?2)?x

?12的定义域。

例3：已知函数f(x)的定义域为(1,4)，求函数f(log2x)的定义域； 变式：已知函数f(2)的定义域为(1,4)，求函数f(x)的定义域。

例4：已知函数f(x)?x?2x?5，求：⑴在R上的值域；⑵x?(?1,3)上的值域； 变式1：⑴求函数y?2x2x2?2x?5的值域；⑵y?log1(x?2x?5)的值域；⑶y?22x2?2x?5的值域。

变式2：求函数y?2x?1?x的值域。

例：1.求下列函数的定义域：

（1）y??x （2）y?x?1?1?x

2x2?3x?2

（3）y?31?1?x （4）y?x2?3?5?x2

Pushing ahead, East, North, West development, facilitating shanty, complete xincheng West Road, stability and reconstruction of the street, Star Ding garden built century Garden District, subject public housing construction, heating the gas expansion accelerated implementation, Jing Rui River and bridge style line solid shaft, further expanded the town development. Beautiful country adhere to the advance and typical for a group to lead. According to \ogical lay based, and industry increased income, and live upgrade civilization, and culture rich connotation\ht, caught built beautiful village, and whole village advance, and easily relocation, and \d three built\oject near 30 a; depth into ecological, and industry, and culture, and tourism, elements, high standards caught party original city Liu, and jade are Xia AO, model village, in province City set has benchmark. Four is equal benefits to promote sharing, coordinated development of various social undertakings. In the case of rigid spending slowing revenue growth, increase, financial 75% to the people's livelihood, the masses have more access in the sharing. Cuoban something good and benefit. Adhere to the affordable, best, carefully cuoban village oil, water and heat, cultural, city and County columns practical, developments benefit families, bring more welfare to the masses. Development of social convenience. Acceptance of balanced development of compulsory education through the national assessment, the County vocational education center was named \chool of vocational education in China\hird batch of national reform and development model through provincial ... Five is to deepen reform and innovation to break bottlenecks and endogenous development of effective fire. As an engine of dynamism, adding reform key to adopting reform measures stress energy and break bottlenecks and promoting development. Pay close attention to the key areas of reform. Conscientiously implement the provincial deployment and cancel, adjustment, to undertake the administrative approval items according to Regulation 347 to further improve administrative efficiency continuing deepening reform for poverty alleviation, speeding up rural land right registration certification pilot project, encouraging the orderly transfer of land management, utilize the land resources, in order to promote scale management laid the Foundation. Actively cultivate the market. Firmly establish a market-oriented, nurturing family farms, industrial users, professional cooperation organization new market management main body 456, effectively improve the industry, intensive and marketization of encouraging support social capital into the small micro-credit, urban development, culture and tourism, public services and other areas, easing development shortfall. To promote mass innovation. o support the rural sector to use new thinking and new ideas, creative work incentives such as actively promoting financial intermediation, bring added 159 in non public enterprises, individually-1540, created a

?x?1?（5）f?x???4x （6）t是时间，距离f?t??60?3t

??3?2x

2.已知函数f?x?的定义域是[-3,0],求函数f?x?1?的定义域。

3.若函数f?x??x?1的定义域是R，求m的取值范围。 2mx?mx?33 练习：

1.求下列函数的定义域：

（1）f?x??4?x?1； （2）f?x??2x2?3x?4

x?1?2

（3）f?x??11?11?1x0?x?1?； （4）f?x??x?x

2.已知f?x?的定义域为?0,1?，求函数y?fx4????f??x??的定义域。

32?? 3 顺义张老师

Pushing ahead, East, North, West development, facilitating shanty, complete xincheng West Road, stability and reconstruction of the street, Star Ding garden built century Garden District, subject public housing construction, heating the gas expansion accelerated implementation, Jing Rui River and bridge style line solid shaft, further expanded the town development. Beautiful country adhere to the advance and typical for a group to lead. According to \ogical lay based, and industry increased income, and live upgrade civilization, and culture rich connotation\ht, caught built beautiful village, and whole village advance, and easily relocation, and \d three built\oject near 30 a; depth into ecological, and industry, and culture, and tourism, elements, high standards caught party original city Liu, and jade are Xia AO, model village, in province City set has benchmark. Four is equal benefits to promote sharing, coordinated development of various social undertakings. In the case of rigid spending slowing revenue growth, increase, financial 75% to the people's livelihood, the masses have more access in the sharing. Cuoban something good and benefit. Adhere to the affordable, best, carefully cuoban village oil, water and heat, cultural, city and County columns practical, developments benefit families, bring more welfare to the masses. Development of social convenience. Acceptance of balanced development of compulsory education through the national assessment, the County vocational education center was named \chool of vocational education in China\hird batch of national reform and development model through provincial ... Five is to deepen reform and innovation to break bottlenecks and endogenous development of effective fire. As an engine of dynamism, adding reform key to adopting reform measures stress energy and break bottlenecks and promoting development. Pay close attention to the key areas of reform. Conscientiously implement the provincial deployment and cancel, adjustment, to undertake the administrative approval items according to Regulation 347 to further improve administrative efficiency continuing deepening reform for poverty alleviation, speeding up rural land right registration certification pilot project, encouraging the orderly transfer of land management, utilize the land resources, in order to promote scale management laid the Foundation. Actively cultivate the market. Firmly establish a market-oriented, nurturing family farms, industrial users, professional cooperation organization new market management main body 456, effectively improve the industry, intensive and marketization of encouraging support social capital into the small micro-credit, urban development, culture and tourism, public services and other areas, easing development shortfall. To promote mass innovation. o support the rural sector to use new thinking and new ideas, creative work incentives such as actively promoting financial intermediation, bring added 159 in non public enterprises, individually-1540, created a三、函数值和函数的值域

例1、求下列函数的值域：（观察法）

x2?4x?35x?1（1）y? （2）y?

2x2?x?14x?2

2x2?4x?7例2.求函数y?2的值域（反解法）

x?2x?3

例3.求函数y?2x?

x?1的值域（配方换元法）

例4.求函数y?5x?14x?2?x?2?的值域（不等式法）

例5.画出函数y?x?4x?6,x??1,5?的图像，并根据其图像写出该函数的值域。（图像法）

2 练习：