《2022年高考數(shù)學(xué)復(fù)習(xí) 專題02 函數(shù)與導(dǎo)數(shù) 函數(shù)的奇偶性與周期性易錯(cuò)點(diǎn)》由會(huì)員分享,可在線閱讀,更多相關(guān)《2022年高考數(shù)學(xué)復(fù)習(xí) 專題02 函數(shù)與導(dǎo)數(shù) 函數(shù)的奇偶性與周期性易錯(cuò)點(diǎn)(2頁(yè)珍藏版)》請(qǐng)?jiān)谘b配圖網(wǎng)上搜索。
1、2022年高考數(shù)學(xué)復(fù)習(xí) 專題02 函數(shù)與導(dǎo)數(shù) 函數(shù)的奇偶性與周期性易錯(cuò)點(diǎn)主標(biāo)題:函數(shù)的奇偶性與周期性易錯(cuò)點(diǎn)副標(biāo)題:從考點(diǎn)分析函數(shù)的奇偶性與周期性易錯(cuò)點(diǎn),為學(xué)生備考提供簡(jiǎn)潔有效的備考策略。關(guān)鍵詞:函數(shù),奇偶性,周期性,易錯(cuò)點(diǎn)難度:3重要程度:5內(nèi)容:【易錯(cuò)點(diǎn)】1對(duì)奇偶函數(shù)的認(rèn)識(shí)及應(yīng)用(1)函數(shù)yx2,x(0,)是偶函數(shù)()(2)偶函數(shù)圖象不一定過原點(diǎn),奇函數(shù)的圖象一定過原點(diǎn)()(3)(教材習(xí)題改編)如果函數(shù)f(x),g(x)為定義域相同的偶函數(shù),則F(x)f(x)g(x)是偶函數(shù)()(4)若函數(shù)yf(xa)是偶函數(shù),則函數(shù)yf(x)關(guān)于直線xa對(duì)稱()(5)已知函數(shù)f(x)為奇函數(shù),且當(dāng)x0時(shí),
2、f(x)x2,則f(1)2.()(6)已知函數(shù)yf(x)是定義在R上的偶函數(shù),且在(,0)上是減函數(shù),若f(a)f(2),則實(shí)數(shù)a的取值范圍是2,2()2對(duì)函數(shù)周期性的理解(7)函數(shù)f(x)在定義域上滿足f(xa)f(x),則f(x)是周期為2a(a0)的周期函數(shù)()(8)若yf(x)既是周期函數(shù),又是奇函數(shù),則其導(dǎo)函數(shù)yf(x)既是周期函數(shù)又是奇函數(shù)()剖析1兩個(gè)防范一是判斷函數(shù)的奇偶性之前務(wù)必先考查函數(shù)的定義域是否關(guān)于原點(diǎn)對(duì)稱,若不對(duì)稱,則該函數(shù)一定是非奇非偶函數(shù),如(1);二是若函數(shù)f(x)是奇函數(shù),則f(0)不一定存在;若函數(shù)f(x)的定義域包含0,則必有f(0)0,如(2)2三個(gè)結(jié)論
3、一是若函數(shù)yf(xa)是偶函數(shù),則函數(shù)yf(x)關(guān)于直線xa對(duì)稱;若函數(shù)yf(xb)是奇函數(shù),則函數(shù)yf(x)關(guān)于點(diǎn)(b,0)中心對(duì)稱,如(4);二是若對(duì)任意xD都有f(xa)f(x),則f(x)是以2a為周期的函數(shù);若對(duì)任意xD都有f(xa)(f(x)0),則f(x)也是以2a為周期的函數(shù),如(7);三是若函數(shù)f(x)既是周期函數(shù),又是奇函數(shù),則其導(dǎo)函數(shù)yf(x)既是周期函數(shù)又是偶函數(shù),如(8)中因?yàn)閥f(x)是周期函數(shù),設(shè)其周期為T,則有f(xT)f(x),兩邊求導(dǎo),得f(xT)(xT)f(x),即f(xT)f(x),所以導(dǎo)函數(shù)是周期函數(shù),又因?yàn)閒(x)是奇函數(shù),所以f(x)f(x),兩邊求導(dǎo),得f(x)(x)f(x)f(x),即f(x)f(x),所以f(x)f(x),所以導(dǎo)函數(shù)是偶函數(shù).