新高考數(shù)學(xué)一輪復(fù)習(xí)提升訓(xùn)練3.2.1 函數(shù)的性質(zhì)（一）（精講）（原卷版）

3.2.1函數(shù)的性質(zhì)（一）（精講）（提升版）思維導(dǎo)圖思維導(dǎo)圖考點(diǎn)呈現(xiàn)考點(diǎn)呈現(xiàn)例題剖析例題剖析考點(diǎn)一單調(diào)區(qū)間（無(wú)參）【例1-1】（2022·貴州）函數(shù)SKIPIF1<0的單調(diào)遞減區(qū)間為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【例1-2】（2022·廣東）函數(shù)SKIPIF1<0的單調(diào)遞增區(qū)間是（

）A．SKIPIF1<0 B．SKIPIF1<0和SKIPIF1<0C．SKIPIF1<0和SKIPIF1<0 D．SKIPIF1<0和SKIPIF1<0【例1-3】（2022·湖北）函數(shù)SKIPIF1<0的單調(diào)遞增區(qū)間是（

）A．SKIPIF1<0SKIPIF1<0 B．SKIPIF1<0SKIPIF1<0C．SKIPIF1<0SKIPIF1<0 D．SKIPIF1<0SKIPIF1<0【例1-4】（2022·山東·濟(jì)南市歷城第二中學(xué)模擬預(yù)測(cè)）函數(shù)SKIPIF1<0在SKIPIF1<0上是減函數(shù)，則實(shí)數(shù)SKIPIF1<0的范圍是_______.【例1-5】（2021·云南昆明市）函數(shù)SKIPIF1<0的單調(diào)增區(qū)間是【一隅三反】1．（2022·全國(guó)·高三專題練習(xí)）函數(shù)SKIPIF1<0的單調(diào)遞增區(qū)間是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．（2022·福建）函數(shù)SKIPIF1<0的單調(diào)減區(qū)間是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2021·全國(guó)·高三階段練習(xí)（文））下列函數(shù)在SKIPIF1<0上是減函數(shù)的為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<04．（2022·全國(guó)·高三專題練習(xí)）函數(shù)SKIPIF1<0的單調(diào)遞增區(qū)間為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<05．（2021·天津靜海區(qū)）函數(shù)SKIPIF1<0的單調(diào)減區(qū)間為___________考點(diǎn)二已知單調(diào)性求參數(shù)【例2-1】（2022·陜西·武功縣普集高級(jí)中學(xué)）已知函數(shù)SKIPIF1<0在SKIPIF1<0，SKIPIF1<0上單調(diào)遞增，在SKIPIF1<0上單調(diào)遞減，則實(shí)數(shù)a的取值范圍為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0【例2-2】（2022·河南濮陽(yáng)·一模）“SKIPIF1<0”是“函數(shù)SKIPIF1<0是在SKIPIF1<0上的單調(diào)函數(shù)”的（

）A．充分不必要條件 B．必要不充分條件C．充要條件 D．既不充分也不必要條件【例2-3】（2022·全國(guó)·高三專題練習(xí)）若函數(shù)SKIPIF1<0（SKIPIF1<0且SKIPIF1<0）在區(qū)間SKIPIF1<0內(nèi)單調(diào)遞增，則SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0已知函數(shù)的單調(diào)性確定參數(shù)的值或范圍要注意以下幾點(diǎn)：已知函數(shù)的單調(diào)性確定參數(shù)的值或范圍要注意以下幾點(diǎn)：若函數(shù)在區(qū)間[a,b]上單調(diào)，則該函數(shù)在此區(qū)間的任意子區(qū)間上也是單調(diào)的；分段函數(shù)的單調(diào)性，除注意各段的單調(diào)性外，還要注意銜接點(diǎn)的取值；（3）復(fù)合函數(shù)的單調(diào)性，不僅要注意內(nèi)外函數(shù)單調(diào)性對(duì)應(yīng)關(guān)系，而且要注意內(nèi)外函數(shù)對(duì)應(yīng)自變量取值范圍溫馨提示【一隅三反】1．（2022·全國(guó)·高三專題練習(xí)）若函數(shù)SKIPIF1<0是SKIPIF1<0上的單調(diào)函數(shù)，則SKIPIF1<0的取值范圍（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2021·全國(guó)·高三專題練習(xí)）已知函數(shù)SKIPIF1<0在SKIPIF1<0上單調(diào)遞減，則實(shí)數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0或SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0或SKIPIF1<0 D．SKIPIF1<03．（2022·重慶）已知函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0，SKIPIF1<0上都單調(diào)遞增，則實(shí)數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<04．（2021·重慶市）已知SKIPIF1<0且SKIPIF1<0，若函數(shù)SKIPIF1<0在SKIPIF1<0上是減函數(shù)，則SKIPIF1<0的取值范圍是__________【答案】SKIPIF1<0考點(diǎn)三奇偶性的判斷【例3】（2022·廣西）下列函數(shù)中，既是奇函數(shù)，又在定義域上單調(diào)遞增的是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【一隅三反】1．（2022·廣東廣州·二模）下列函數(shù)中，既是偶函數(shù)又在SKIPIF1<0上單調(diào)遞增的是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．（2022·河南）下列函數(shù)中，即是奇函數(shù)又是單調(diào)函數(shù)的是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．（2022·安徽）設(shè)函數(shù)SKIPIF1<0,SKIPIF1<0的定義域?yàn)镽，且SKIPIF1<0是奇函數(shù)，SKIPIF1<0是偶函數(shù)，則下列結(jié)論中正確的是（）A．SKIPIF1<0是偶函數(shù) B．SKIPIF1<0是奇函數(shù)C．SKIPIF1<0是奇函數(shù) D．SKIPIF1<0是奇函數(shù)考點(diǎn)四奇偶性的應(yīng)用【例4-1】（2021·河南）已知SKIPIF1<0為奇函數(shù)，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，則當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0【例4-2】（2022·河南洛陽(yáng)）若函數(shù)SKIPIF1<0是偶函數(shù)，則SKIPIF1<0（

）A．-1 B．0 C．1 D．SKIPIF1<0【一隅三反】1．（2022·全國(guó)·高三專題練習(xí)）已知函數(shù)SKIPIF1<0是偶函數(shù)，則SKIPIF1<0的值是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．1 D．22．（2022·江西）若函數(shù)SKIPIF1<0為偶函數(shù)，則實(shí)數(shù)SKIPIF1<0（

）A．SKIPIF1<0 B．3 C．SKIPIF1<0 D．93．（2022·全國(guó)·高三專題練習(xí)）已知函數(shù)SKIPIF1<0是偶函數(shù)，則SKIPIF1<0，SKIPIF1<0的值可能是（

）A．SKIPIF1<0，SKIPIF1<0 B．SKIPIF1<0，SKIPIF1<0C．SKIPIF1<0，SKIPIF1<0 D．SKIPIF1<0，SKIPIF1<04．（2021·河北）已知函數(shù)SKIPIF1<0是SKIPIF1<0上的奇函數(shù)，當(dāng)SKIPIF1<0時(shí)，SKIPIF1<0，則函數(shù)的解析式為SKIPIF1<0______．考點(diǎn)五單調(diào)性與奇偶性應(yīng)用之比較大小【例5-1】（2022·安徽·壽縣第一中學(xué)）若SKIPIF1<0為定義在SKIPIF1<0上的偶函數(shù)，且在SKIPIF1<0上單調(diào)遞減，則（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0【例5-2】（2022·重慶·西南大學(xué)附中模擬預(yù)測(cè)）設(shè)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則a，b，c的大小關(guān)系是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0【一隅三反】1．（2022·天津河北·二模）已知SKIPIF1<0是定義在R上的偶函數(shù)，且在區(qū)間SKIPIF1<0單遞調(diào)減，若SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則a，b，c的大小關(guān)系為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．（2022·安徽·巢湖市第一中學(xué)高三期中（理））已知函數(shù)SKIPIF1<0，設(shè)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則a，b，c的大小關(guān)系為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．（2022云南德宏））已知函數(shù)SKIPIF1<0是定義在SKIPIF1<0上的偶函數(shù)，對(duì)任意SKIPIF1<0，SKIPIF1<0，都有SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．（2022·湖北·荊門市龍泉中學(xué)一模）設(shè)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，則下列關(guān)系正確的是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0考點(diǎn)六單調(diào)性與奇偶性應(yīng)用之解不等式【例6-1】（2022·安徽馬鞍山）已知偶函數(shù)SKIPIF1<0在SKIPIF1<0上單調(diào)遞增，且SKIPIF1<0，則不等式SKIPIF1<0的解集為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【例6-2】（2022·安徽·）已知SKIPIF1<0是奇函數(shù)，若SKIPIF1<0恒成立，則實(shí)數(shù)SKIPIF1<0的取值范圍是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【一隅三反】1．（2022·云南昭通）若定義在SKIPIF1<0上的奇函數(shù)SKIPIF1<0在SKIPIF1<0上單調(diào)遞增，且SKIPIF1<0，則不等式SKIPIF1<0的解集為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．（2022·河南）已知定義在R上的函數(shù)SKIPIF1<0為奇函數(shù)，則