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2019-2020数学人教A版必修一高一数学《2.1.2-2指数函数的性质》课件优质课件_图文

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2.1.2 指数函数及其性质
第二课时 指数函数的性质

问题提出
1.什么是指数函数?其定义域是什么?大致 图象如何?
2.任何一类函数都有一些基本性质,那么指 数函数具有那些基本性质呢?

知识探究(一):函数 y ? ax (a ? 1) 的性质
y
考察函数 y ? ax (a ? 1) 的图象:
1

0

x

思考1:函数图象分布在那些象限?与x轴的相 对位置关系如何?

思考2:由此可知函数的定义域、值域分别是 什么?

考察函数 y ? ax (a ? 1)

y

的图象:

1

0

x

思考3:函数图象的升降情况如何?由此说明 什么性质?

思考4:图象在y轴左、右两侧的分布情况如何? 由此说明函数值有那些变化?

思考5:若a>b>1,则函数 y ? ax与 y ? bx 的
图象的相对位置关系如何?

y ? ax
y

y ? bx

1

0

x

知识探究(二):函数 y ? ax (0 ? a ? 1) 的性质

考察函数 y ? ax (0 ? a ? 1)

y

的图象:
1

0

x

思考1:函数的定义域、值域、单调性、函数 值分布分别如何?

思考2:若0<b<a<1,则函数 y ? ax 与
y ? bx的图象的相对位置关系如何?

y ? bx y
y ? ax
1

0

x

思考3:指数函数具有奇偶性吗?
思考4:指数函数存在最大值和最小值 吗?
思考5:设a>0,a≠1,若am=an,则m与n的大 小关系如何?若am>an,则m与n的大小关系如 何?

理论迁移
例1 比较下列各题中两个值的大小 (1) 1.72.5与1.73; (2) 0.8-0.1与0.8-0.2 ; (3) 1.70.3与0.93.1
例2 若指数函数y=(2a-1)x是减函数, 求实数a的取值范围.

例3 确定函数f(x)= 2-|x|的单调区间和 值域.
例4 设 a = 0.9m ? 0.8n ,
b = 0.9n ? 0.8m ,
其中m,n为实数,试比较a与b的大小.

作业 P59习题2.1A组:7,8,9.


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