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北师大版必修一《简单的幂函数》word教案

北师大版必修一《简单的幂函数》word教案
北师大版必修一《简单的幂函数》word教案

简单的幂函数

学习目标:

1、 了解指数是整数的简单幂函数的概念,能够判断幂函数;

2、 会利用定义判定、证明简单函数的奇偶性;

3、 了解利用奇偶性画函数图像和研究函数的方法。 学习重点:

幂函数的概念;奇偶性的定义及简单函数奇偶性的判定与证明。 难点:

利用奇偶性画函数图像和研究函数 学习过程: 一、

引入:我们已经很熟悉y=x 是正比例函数,y=x 2

是二次函数, y=

x

1 (即y=x -1)是反比例函数,它们有什么共同特点呢?根据这一特点它们有个怎样的共同名字? 二、 阅读导学 阅读P 481,2两段,

1、回答:一般的,函数 叫做幂函数,其中 是自变量, 是常数。

2、判断下列函数,其中那些是幂函数:

y=x 3

,y=x 2

+x , y=2x 2

, y=(2x)4

幂函数的系数是 底数是 , 是任意实数。 例1画出函数f(x)= x 3

的图像,讨论其单调性。

再用描点法画出图像: 从图像上可以看出f(x)= x 3

是R 上的 函数

阅读P 48

3、观察f(x)= x 3的图像,说出他有那些特征?什么是奇函数?奇函数满足关系式 ?

4、观察f(x)= x 2的图像说出他有那些特征?什么是偶函数?偶函数满足关系式 ?

例2判断f(x)= -2x 2和g(x)= x 4

+2的奇偶性 方法小结:

三、 动手实践

在P 49图2-28中,只画出了函数图像的一半,请你画出它们的另一半,并说出画法的依据 结论:

四、 自我展示

1、下列函数中是幂函数的是( )

①y=21x

②y=ax m (a,m 为非零常数,且a ≠1)③y=x 31

+ x 2④y= x π⑤y=(x-1)3

2、画出下列函数图像,判断奇偶性 f(x)= -x

3 y=x 2

,x ∈(]33-, f(x)=3x 2-3 f(x)=2(x+1)2+1 五、

拓展练习

1.已知y=(m 2

+2m-2)x 1

1

2

-m

+2n-3是幂函数,求m,n 的值。

2.函数y=f(x)是奇函数,在[a,b]上是减少的,则它在[-b,-a]上是( ) A.增加的 B .减少的 C.先增后减 D.先减后增

3已知函数f(x)=(m-1)x2+2mx+3是偶函数 ,则f(x)在(-∞,0]上是( ) A.增加的 B .减少的 C.先增后减 D.先减后增 六、 课后小结

七、 作业

P 50A 组2,3(1)(3)

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