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https.//www.ae523.com/enter/an...www.:浙江省台州市高二数学下学期 第4讲 函数的奇偶性与周期性学案(无答案)文

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第四讲 函数的奇偶性与周期性

学习目标 1.结合具体函数,了解函数的奇偶性的含义; 2.会运用函数的图象理解和研究函数的奇偶性; 3.了解函数周期性、最小正周期的含义,会判断、应用简单函数的周期性。 知识梳理: 考点一:函数的奇偶性判断与应用:(定义法;图象法;性质法) 例 1.判断下列函数的奇偶性

(1) f (x) ? 3 ? x2 ? x2 ? 3 ; (2) f (x) ? (x ?1) 1? x ; (3) f (x) ? 4 ? x2

1? x

x?3 ?3

考点二:函数的单调性与奇偶性:
例 2.函数 y ? f (x) 是 (?1,1) 上是减函数且为奇函数,满足 f (a2 ? a ?1) ? f (a ? 2) ? 0 ,

求实数 a 的取值范围.

(1, 3)

变式:设定义在[?2, 2] 上的偶函数 f (x) 的区间[0, 2] 上单调递减,若 f (1? m) ? f (m) ,



实数 m 的取值范围

[?1, 1) 2

考点三:函数的单调性与奇偶性周期性综合应用:

例 3:已知函数是 f (x) 是 (??, ??) 上的偶函数,若对于 x ? 0 ,都有 f (x ? 2) ? f (x) ,且

当 x ?[0, 2) 时, f (x) ? 2x ,则 f (?2014) ? f (2015) 的值是( )

A .1 变式:

B. 2

C .3

D.4


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