一次函数讲义与练习

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1、专业好文档一次函数一、函数及其相关概念1常量与变量：在某一变化过程中，可以取不同数值的量叫做变量；在某一变化过程中保持数值不变的量叫做常量2函数：在某一变化过程中的两个变量x和y，如果对于x在某一范围内的每一个确定的值，y都有唯一确定的值和它对应，那么y就叫做x的函数，其中x做自变量，y是因变量(1)自变量取值范围的确定整式函数自变量的取值范围是全体实数分式函数自变量的取值范围是使分母不为0的实数二次根式函数自变量的取值范嗣是使被开方数是非负数的实数，若涉及实际问题的函数，除满足上述要求外还要使实际问题有意义(2)函数值：对于自变量在取值范围内的一个值所求得的函数的对应值3函数常用的表示方法：

2、(1)图象法：形象、直观；(2)列表法：具体、准确；(3)解析法：抽象、全面。由函数的解析式作函数的图象，一般步骤是：列表、描点、连线范例讲解例1、一汽车油箱中有油30升，若每小时耗油10升。(1)写出油箱中剩油量Q(升)与时间t(小时)之间的函数关系式；(2)指出其常数、自变量、因变量；(3)Q是t的函数吗？为什么？1、设路程为s，时间为t，速度为v，当v=60时，路程和时间的关系式为 ，这个关系式中， 是常量， 是变量， 是 的函数。2、下列各表达式不是表示y是x的函数的是( )3、如果每盒圆珠笔12支，售价18元，那么，圆珠笔的总售价y(元)与圆珠笔的支数x(支)之间的函数关系式是( )

3、二、一次函数（一）、正比例函数和一次函数的概念一般地，如果（k，b是常数，k0），那么y叫做x的一次函数。特别地，当一次函数中的b为0时，（k为常数，k0）。这时，y叫做x的正比例函数。写出下列各题中y与x之间的关系式，并判断：y是否为x的一次函数？是否为正比例函数？ (1)汽车以60千米/时的速度匀速行驶,行驶路程为y(千米)与行驶时间x(时)之间的关系;(2)圆的面积y (c m2)与它的半径x ( cm)之间的关系;(3)一棵树现在高5 0 厘米，每个月长高2 厘米，x 月后这棵树的高度为y 厘米。(二)、一次函数的图像和性质1.有下列函数：y=6x-5 , y=5x, , y=x+4,

4、 y=-4x+3其中过原点的直线是_；函数y随x的增大而增大的是_；函数y随x的增大而减小的是_；图象过第一、二、三象限的是_。2、对于函数y5x+6，y的值随x值的减小而_。3、对于函数, y的值随x值的_而增大。 （三）、正比例函数和一次函数解析式的确定确定一个正比例函数，就是要确定正比例函数定义式（k0）中的常数k。确定一个一次函数，需要确定一次函数定义式（k0）中的常数k和b。（解这类问题的一般方法是待定系数法。）方法：待定系数法：设；代；解；还原 依据两个独立的条件确定k,b的值，即可求解出一次函数y=kx+b（k0）的解析式。 已知是直线或一次函数可以设y=kx+b（k0）； 若点

5、在直线上，则可以将点的坐标代入解析式构建方程。例、已知一次函数y=kx+b(k0)在x=1时，y=5，且它的图象与x轴交点的横坐标是，求这个一次函数的解析式。解：设一次函数解析式为y=kx+b，把x=1时， y=5；x=6时，y=0代入解析式，得 解得 一次函数的解析式为y= - x+6。1、当k_时，是一次函数；2、当m_时，是一次函数；3、当m_时，是一次函数；4、如果一次函数y=kx-3k+6的图象经过原点，那么k的值为_。5、已知y-1与x成正比例，且x=2时，y=4，那么y与x之间的函数关系式为_。练习1、若函数y=3x+b经过点（2，-6），求函数的解析式。2、直线y=kx+b的图

6、像经过A（3，4）和点B（2，7），3、某植物栽t天后的高度为ycm,图中反映了y与t之间的关系，根据图象回答下列问题： (1)植物刚栽的时候多高？（2）3天后该植物高度为多少？（3）几天后该植物高度可达21cm? （4）先写出y与t的关系式，再计算长到100cm需几天？4、甲、乙两人进行百米赛跑，甲比乙跑得快如果两人同时起跑，甲肯定赢现在甲让乙先跑若干米图中l1，l2分别表示两人的路程s（米）与时间t（秒）的关系（1）哪条线表示甲的路程与时间的关系；（2）甲让乙先跑了多少米？（3）谁先到达终点？Winger Tuivasa-Sheck, who scored two tries in the

7、 Kiwis 20-18 semi-final win over England, has been passed fit after a lower-leg injury, while Slater has been named at full-back but is still recovering from a knee injury aggravated against USA.Both sides boast 100% records heading into the encounter but Australia have not conceded a try since Josh

8、 Charnleys effort in their first pool match against England on the opening day.Aussie winger Jarryd Hayne is the competitions top try scorer with nine, closely followed by Tuivasa-Sheck with eight.But it is recently named Rugby League International Federation player of the year Sonny Bill Williams w

9、ho has attracted the most interest in the tournament so far.The Kiwi - with a tournament high 17 offloads - has the chance of becoming the first player to win the World Cup in both rugby league and rugby union after triumphing with the All Blacks in 2011.Id give every award back in a heartbeat just

10、to get across the line this weekend, said Williams.The (lack of) air up there Watch mCayman Islands-based Webb, the head of Fifas anti-racism taskforce, is in London for the Football Associations 150th anniversary celebrations and will attend Citys Premier League match at Chelsea on Sunday.I am goin

11、g to be at the match tomorrow and I have asked to meet Yaya Toure, he told BBC Sport.For me its about how he felt and I would like to speak to him first to find out what his experience was.Uefa hasopened disciplinary proceedings against CSKAfor the racist behaviour of their fans duringCitys 2-1 win.

12、Michel Platini, president of European footballs governing body, has also ordered an immediate investigation into the referees actions.CSKA said they were surprised and disappointed by Toures complaint. In a statement the Russian side added: We found no racist insults from fans of CSKA. Baumgartner t

13、he disappointing news: Mission aborted.The supersonic descent could happen as early as Sunda.The weather plays an important role in this mission. Starting at the ground, conditions have to be very calm - winds less than 2 mph, with no precipitation or humidity and limited cloud cover. The balloon, w

14、ith capsule attached, will move through the lower level of the atmosphere (the troposphere) where our day-to-day weather lives. It will climb higher than the tip of Mount Everest (5.5 miles/8.85 kilometers), drifting even higher than the cruising altitude of commercial airliners (5.6 miles/9.17 kilo

15、meters) and into the stratosphere. As he crosses the boundary layer (called the tropopause),e can expect a lot of turbulence.The balloon will slowly drift to the edge of space at 120,000 feet ( Then, I would assume, he will slowly step out onto something resembling an Olympic diving platform.They bl

16、ew it in 2008 when they got caught cold in the final and they will not make the same mistake against the Kiwis in Manchester.Five years ago they cruised through to the final and so far history has repeated itself here - the last try they conceded was scored by Englands Josh Charnley in the opening g

17、ame of the tournament.That could be classed as a weakness, a team under-cooked - but I have been impressed by the Kangaroos focus in their games since then.They have been concentrating on the sort of stuff that wins you tough, even contests - strong defence, especially on their own goal-line, comple

18、ting sets and a good kick-chase. Theyve been great at all the unglamorous stuff that often goes unnoticed in the stands but not by your team-mates.It is as though their entire tournament has been preparation for the final.In Johnathan Thurston, Cooper Cronk, Cameron Smith and either Billy Slater or

19、Greg Inglis at full-back they have a spine that is unmatched in rugby league. They have played in so many high-pressure games - a priceless asset going into Saturday.The Kiwis are a lot less experienced but winning a dramatic match like their semi-final against England will do wonders for their confidence.They defeated Australia in the Four Nations final in 2010 and the last World Cup, and know they can rise to the big occasion.