2．1．对称性+奇偶性周期性

性质3 如果f(x)是奇函数，且图像关于x=a对称，则得f(x)是以T=2a为周期的周期函数。

证明：f(x)的图像关于x=a对称

推论3.1一般地，若定义在R上的函数f(x)的图象关于直线x=a和x=b()对称，则f(x)是以为周期的周期函数。

证明：

2.　　　　 奇偶性、对称性、周期性三者之间的联系(为了减少讨论，以下提到的f(x)的定义域默认为关于原点对称)

1.　　 应用定义探究周期规律

(1).定义：若函数对定义域中任意x均有f(x+T)= f(x)(T为不等于0的常数)，则f(x)为周期函数。

性质1.f(x)是T=2a的周期函数的充要条件是f(x+a)=f(x-a)

证明：(必要性)

(充分性)

推论1.1 若f(a +x)=-f(x)，则f(x)的周期T=2a

推论1.2 若f(a +x)=1/f(x)，则f(x)的周期T=2a

(2)函数奇偶性的定义与函数图像的对称性

奇函数：如果对于函数定义域内任意一个数x，都有f(-x)=-f(x)，那么，函数f(x)就是奇函数。

偶函数：如果对于函数定义域内任意一个数x，都有f(-x)=f(x)，那么，函数f(x)就是偶函数。

轴对称：如果函数f(x)满足f(x+a)=f(a-x)，则f(x)的图像关于x=a对称

中心对称：如果函数f(x)满足f(x+a)=-f(a-x)，则f(x)的图像关于(a,0)对称

性质2.设a，b是任意常数，则函数f(a+x)=f(b-x)的充要条件是f(x)的图像关于对称

证明：(必要性)

　　 (充分性)

推论2.1.偶函数的图像关于y轴对称，奇函数的图像关于原点对称

3. 你的看法……。

One possible version

It is generally believed that different people have different habits. Some people are addicted to habits like drinking and smoking, while others pay special attention to healthy diet and never taste things like alcohol and cigarettes.

It goes without saying that there is close relationship between personal habits and public health. On the one hand, good habits serve as the necessary basis of public health, that is to say, without good habits, public health can’t be guaranteed. On the other hand, infectious disease is the natural result brought by dirty habits, like AIDS, SARS, H1N1 flu and so on.

Personally, I think it is high time we placed emphasis on improving personal habits and public health. If we mind our manners and behave ourselves well, there must be a bright and encouraging future.

2. 习惯与卫生的关系：习惯是卫生基础; 不好的习惯，会导致一些传染疾病传播，如AIDS，SARS， H1N1流感等。

1. 介绍有些人不同的好习惯和坏习惯。

25.不同人都有着不同的习惯，个人习惯直接关系着公共卫生。请根据下列要求，写一篇120字的英语短文，开头和结尾已经写好，不计入总词数。

4. 文章的开头已给出, 不计入总词数。

参考词汇: 猪流感swine flu; 口罩 face mask.

Swine flu has come to our School! However, there is no vaccine to protect its virus. How do we protect us from it?

One possible version

Swine flu has come to our School! However, there is no vaccine to protect its virus. How do we protect us from it?

We advise that you should wear face mask and avoid going to the crowded place when you go out. We remember not to be in close contact with the patients infected with swine flu. On the other hand, the best way to stay away from this virus is to wash your hands often, and make sure that you have enough sleep. At the same time, we should do more exercise so that we can build up our body.

We are sure that we must overcome the threat against swine flu as long as we take proper measures and insist on taking exercise every day.

3. 词数: 120字左右