新高考數(shù)學二輪復習易錯點02 函數(shù)的性質（原卷版）

易錯點02函數(shù)的性質易錯題【01】不理解函數(shù)概念在函數(shù)f：A→B中SKIPIF1<0都是非空數(shù)集,且滿足兩允許,兩不允許：允許B中有剩余元素,不允許A中有剩余元素；允許多對一,不允許一對多.易錯題【02】研究函數(shù)單調性忽略定義域研究函數(shù)的單調性切記定義域優(yōu)先,分式形式的函數(shù)要保證分母不為零,對數(shù)型函數(shù)要保證底數(shù)大于零且不等于1,真數(shù)大于零.易錯題【03】研究函數(shù)奇偶性與單調性忽略其等價形式的應用1.注意與函數(shù)奇偶性有關的幾個結論：(1)SKIPIF1<0是偶函數(shù)SKIPIF1<0SKIPIF1<0；(2)SKIPIF1<0是奇函數(shù)SKIPIF1<0SKIPIF1<0；(3)若函數(shù)SKIPIF1<0在SKIPIF1<0處有意義,則SKIPIF1<0；(4)SKIPIF1<0是偶函數(shù),則SKIPIF1<0,SKIPIF1<0是偶函數(shù),則SKIPIF1<0.2.增函數(shù)與減函數(shù)的等價形式(1)若SKIPIF1<0,且SKIPIF1<0,SKIPIF1<0SKIPIF1<0SKIPIF1<0在SKIPIF1<0上是增函數(shù)；SKIPIF1<0SKIPIF1<0SKIPIF1<0在SKIPIF1<0上是減函數(shù).(2)若SKIPIF1<0,且SKIPIF1<0,則SKIPIF1<0是增函數(shù).易錯題【04】不會利用對稱性與奇偶性推導函數(shù)的周期性(1)函數(shù)SKIPIF1<0滿足SKIPIF1<0(SKIPIF1<0),若SKIPIF1<0為奇函數(shù),則其周期為SKIPIF1<0,若SKIPIF1<0為偶函數(shù),則其周期為SKIPIF1<0.(2)函數(shù)SKIPIF1<0SKIPIF1<0的圖象關于直線SKIPIF1<0和SKIPIF1<0SKIPIF1<0都對稱,則函數(shù)SKIPIF1<0是以SKIPIF1<0為周期的周期函數(shù)；函數(shù)SKIPIF1<0SKIPIF1<0的圖象關于兩點SKIPIF1<0、SKIPIF1<0SKIPIF1<0都對稱,則函數(shù)SKIPIF1<0是以SKIPIF1<0為周期的周期函數(shù)；函數(shù)SKIPIF1<0SKIPIF1<0的圖象關于SKIPIF1<0和直線SKIPIF1<0SKIPIF1<0都對稱,則函數(shù)SKIPIF1<0是以SKIPIF1<0為周期的周期函數(shù). 01下列四個圖像中,是函數(shù)圖像的是()A．(1)(2) B．(1)(2)(3) C．(1)(3)(4) D．(1)(2)(3)(4)1.函數(shù)y=f(x)的圖象與直線SKIPIF1<0的交點個數(shù)()A．至少1個 B．至多1個 C．僅有1個D．有0個、1個或多個2.下列四個圖像中,不是函數(shù)圖像的是()A． B．C． D． 02(2022湖北省武漢市高三上學期月考)函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上單調遞增,則實數(shù)SKIPIF1<0的取值范圍為()．A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<01.函數(shù)SKIPIF1<0的單調遞增區(qū)間為____________．2.(2022屆安徽省安慶市重點高中高三上學期月考)函數(shù)SKIPIF1<0在SKIPIF1<0單調遞增,求a的取值范圍()A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0 03(2015新課標全國卷1)若函數(shù)SKIPIF1<0為偶函數(shù),則SKIPIF1<0=1．(2022屆陜西省西安高三上學期期中)已知函數(shù)SKIPIF1<0(SKIPIF1<0,SKIPIF1<0),且SKIPIF1<0,則SKIPIF1<0()A．SKIPIF1<0 B．2 C．1 D．SKIPIF1<02．(2022屆北京市通州區(qū)高三上學期期中)已知函數(shù)SKIPIF1<0的定義域為SKIPIF1<0,SKIPIF1<0,SKIPIF1<0是偶函數(shù),SKIPIF1<0,有SKIPIF1<0,則()A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0 04(202全國卷甲卷理數(shù)12)設函數(shù)SKIPIF1<0的定義域為SKIPIF1<0,SKIPIF1<0為奇函數(shù),SKIPIF1<0為偶函數(shù),當SKIPIF1<0,SKIPIF1<0時,SKIPIF1<0．若SKIPIF1<0(3)SKIPIF1<0,則SKIPIF1<0SKIPIF1<0A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<01．(2022屆江西省贛州市十七校高三上學期期中聯(lián)考)已如SKIPIF1<0的圖像關于點SKIPIF1<0對稱,且對SKIPIF1<0,都有SKIPIF1<0成立,當SKIPIF1<0時,SKIPIF1<0,則SKIPIF1<0()A．SKIPIF1<0 B．2 C．0 D．SKIPIF1<02.(多選題)(2022屆山東師范大學附屬中學高三上學期月考)定義在SKIPIF1<0的奇函數(shù)SKIPIF1<0滿足SKIPIF1<0,當SKIPIF1<0時SKIPIF1<0,則以下結論正確的有()A．SKIPIF1<0的周期為6 B．SKIPIF1<0的圖象關于SKIPIF1<0對稱C．SKIPIF1<0 D．SKIPIF1<0的圖象關于SKIPIF1<0對稱錯1．(2022北京市朝陽區(qū)高三上學期期中屆)若函數(shù)SKIPIF1<0為奇函數(shù),則實數(shù)SKIPIF1<0().A．SKIPIF1<0 B．SKIPIF1<0 C．0 D．12．(2022屆廣東省深圳實驗學校、湖南省長沙市第一中學高三上學期聯(lián)考)已知函數(shù)SKIPIF1<0,若不等式SKIPIF1<0在SKIPIF1<0上有解,則實數(shù)a的取值范圍是()A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．已知偶函數(shù)SKIPIF1<0的圖象經(jīng)過點SKIPIF1<0,且當SKIPIF1<0時,不等式SKIPIF1<0恒成立,則使得SKIPIF1<0成立的SKIPIF1<0取值范圍為()A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．(2022屆新疆克拉瑪依市高三第三次模擬)已知定義在R上的奇函數(shù)SKIPIF1<0滿足SKIPIF1<0,當SKIPIF1<0時,SKIPIF1<0,若函數(shù)SKIPIF1<0的所有零點為SKIPIF1<0,當SKIPIF1<0時,SKIPIF1<0()A．20 B．24 C．28 D．365．(2022屆重慶市涪陵實驗中學校高三上學期期中)已知SKIPIF1<0的圖象關于點SKIPIF1<0對稱,且對SKIPIF1<0,都有SKIPIF1<0成立,當SKIPIF1<0時,SKIPIF1<0,則SKIPIF1<0()A．SKIPIF1<0 B．SKIPIF1<0 C．0 D．26．(2022屆吉林省長春市重點高中高三上學期月考)已知函數(shù)f(x)＝lg(x2－2x－3)在(－∞,a)單調遞減,則a的取值范圍是()A．(－∞,－1] B．(－∞,2] C．[5,＋∞) D．[3,＋∞)7．(多選題)(2022屆決勝新高考名校交流高三聯(lián)考卷)SKIPIF1<0是定義在SKIPIF1<0上的偶函數(shù),對SKIPIF1<0,均有SKIPIF1<0,當SKIPIF1<0時,SKIPIF1<0,則下列結論正確的是()A．函數(shù)SKIPIF1<0的一個周期為SKIPIF1<0 B．SKIPIF1<0C．當SKIPIF1<0時,SKIPIF1<0 D．函數(shù)SKIPIF1<0在SKIPIF1<0內(nèi)有SKIPIF1<0個零點8．(2022屆廣東省普通高中高三上學期11月階段性檢測)已知定義在SKIPIF1<0上的函數(shù)SKIPIF1<0滿足SKIPIF1<0,且SK