高一數(shù)學(xué)必修一函數(shù)周期性和奇偶性經(jīng)典題型

1、1函數(shù)的奇偶性與周期性提高精講奇函數(shù)偶函數(shù)如果對(duì)于函數(shù)f(x)的定義域內(nèi)的任意一個(gè)x(定義域關(guān)于原點(diǎn)對(duì)稱)定義都有f(－x)＝－f(x)，那么函數(shù)f(x)是函數(shù)都有f(－x)＝f(x)，那么函數(shù)f(x)是函數(shù)特點(diǎn)圖象關(guān)于對(duì)稱圖象關(guān)于軸對(duì)稱1.函數(shù)f(x)＝0，x∈R既是奇函數(shù)又是偶函數(shù)2.奇偶函數(shù)常用結(jié)論f(x)g(x)f(x)g(x)f(x)g(x)f(x)g(x)f(g(x))偶函數(shù)偶函數(shù)偶函數(shù)偶函數(shù)奇函數(shù)偶函數(shù)奇函數(shù)偶函數(shù)偶函數(shù)奇

2、函數(shù)奇函數(shù)奇函數(shù)3.周期函數(shù)：對(duì)于函數(shù)y＝f(x)，如果存在一個(gè)非零常數(shù)T，使得當(dāng)x取定義域內(nèi)的任何值時(shí)，都有f(x＋T)＝f(x)，那么就稱函數(shù)y＝f(x)為周期函數(shù)，稱T為這個(gè)函數(shù)的周期4.周期函數(shù)常見結(jié)論：(1)若f(x＋a)＝f(x－a)，則函數(shù)的周期為2a.(2)若f(x＋a)＝－f(x)，則函數(shù)的周期為2a.(3)若f(xa)=(a0)則函數(shù)的周期為2a.??xf1(4)若f(x＋a)＝－，則函數(shù)的周期為2a.??xf15.

3、對(duì)稱函數(shù)（引申知識(shí)點(diǎn)）如果函數(shù)滿足，則函數(shù)的圖象關(guān)于直線對(duì)稱.??yfx?????faxfbx?????yfx?2abx??【考法一奇偶性與不等式】1.若函數(shù)f(x)＝是奇函數(shù)，則使f(x)3成立的x的取值范圍為()2x＋12x－aA(－∞，－1)B(－10)C(01)D(1，＋∞)【考法二求解析式】3Aab＝cBba＝cCbcaDacb3.設(shè)f(x)是定義在R上的以3為周期的奇函數(shù)，若f(2)1，f(2014)＝，則實(shí)數(shù)a的取值范2a