新高考數(shù)學(xué)一輪復(fù)習(xí)講練測(cè)第2章第06講 函數(shù)的圖象（講義）（原卷版）

第06講函數(shù)的圖象一、掌握基本初等函數(shù)的圖像（1）一次函數(shù)；（2）二次函數(shù)；（3）反比例函數(shù)；（4）指數(shù)函數(shù)；（5）對(duì)數(shù)函數(shù)；（6）三角函數(shù)．二、函數(shù)圖像作法1、直接畫①確定定義域；②化簡(jiǎn)解析式；③考察性質(zhì)：奇偶性（或其他對(duì)稱性）、單調(diào)性、周期性、凹凸性；④特殊點(diǎn)、極值點(diǎn)、與橫/縱坐標(biāo)交點(diǎn)；⑤特殊線（對(duì)稱軸、漸近線等）．2、圖像的變換（1）平移變換①函數(shù)SKIPIF1<0的圖像是把函數(shù)SKIPIF1<0的圖像沿SKIPIF1<0軸向左平移SKIPIF1<0個(gè)單位得到的；②函數(shù)SKIPIF1<0的圖像是把函數(shù)SKIPIF1<0的圖像沿SKIPIF1<0軸向右平移SKIPIF1<0個(gè)單位得到的；③函數(shù)SKIPIF1<0的圖像是把函數(shù)SKIPIF1<0的圖像沿SKIPIF1<0軸向上平移SKIPIF1<0個(gè)單位得到的；④函數(shù)SKIPIF1<0的圖像是把函數(shù)SKIPIF1<0的圖像沿SKIPIF1<0軸向下平移SKIPIF1<0個(gè)單位得到的；（2）對(duì)稱變換①函數(shù)SKIPIF1<0與函數(shù)SKIPIF1<0的圖像關(guān)于SKIPIF1<0軸對(duì)稱；函數(shù)SKIPIF1<0與函數(shù)的圖像關(guān)于SKIPIF1<0軸對(duì)稱；函數(shù)SKIPIF1<0與函數(shù)SKIPIF1<0的圖像關(guān)于坐標(biāo)原點(diǎn)SKIPIF1<0對(duì)稱；②若函數(shù)SKIPIF1<0的圖像關(guān)于直線SKIPIF1<0對(duì)稱，則對(duì)定義域內(nèi)的任意SKIPIF1<0都有SKIPIF1<0或SKIPIF1<0（實(shí)質(zhì)上是圖像上關(guān)于直線SKIPIF1<0對(duì)稱的兩點(diǎn)連線的中點(diǎn)橫坐標(biāo)為SKIPIF1<0，即SKIPIF1<0為常數(shù)）；若函數(shù)SKIPIF1<0的圖像關(guān)于點(diǎn)SKIPIF1<0對(duì)稱，則對(duì)定義域內(nèi)的任意SKIPIF1<0都有SKIPIF1<0③SKIPIF1<0的圖像是將函數(shù)SKIPIF1<0的圖像保留SKIPIF1<0軸上方的部分不變，將SKIPIF1<0軸下方的部分關(guān)于SKIPIF1<0軸對(duì)稱翻折上來得到的（如圖（a）和圖（b））所示④SKIPIF1<0的圖像是將函數(shù)SKIPIF1<0的圖像只保留SKIPIF1<0軸右邊的部分不變，并將右邊的圖像關(guān)于SKIPIF1<0軸對(duì)稱得到函數(shù)SKIPIF1<0左邊的圖像即函數(shù)SKIPIF1<0是一個(gè)偶函數(shù)（如圖（c）所示）．注：SKIPIF1<0的圖像先保留SKIPIF1<0原來在SKIPIF1<0軸上方的圖像，做出SKIPIF1<0軸下方的圖像關(guān)于SKIPIF1<0軸對(duì)稱圖形，然后擦去SKIPIF1<0軸下方的圖像得到；而SKIPIF1<0的圖像是先保留SKIPIF1<0在SKIPIF1<0軸右方的圖像，擦去SKIPIF1<0軸左方的圖像，然后做出SKIPIF1<0軸右方的圖像關(guān)于SKIPIF1<0軸的對(duì)稱圖形得到．這兩變換又叫翻折變換．⑤函數(shù)SKIPIF1<0與SKIPIF1<0的圖像關(guān)于SKIPIF1<0對(duì)稱．（3）伸縮變換①SKIPIF1<0的圖像，可將SKIPIF1<0的圖像上的每一點(diǎn)的縱坐標(biāo)伸長(zhǎng)SKIPIF1<0或縮短SKIPIF1<0到原來的SKIPIF1<0倍得到．②SKIPIF1<0的圖像，可將SKIPIF1<0的圖像上的每一點(diǎn)的橫坐標(biāo)伸長(zhǎng)SKIPIF1<0或縮短SKIPIF1<0到原來的SKIPIF1<0倍得到．【解題方法總結(jié)】（1）若SKIPIF1<0恒成立，則SKIPIF1<0的圖像關(guān)于直線SKIPIF1<0對(duì)稱．（2）設(shè)函數(shù)SKIPIF1<0定義在實(shí)數(shù)集上，則函數(shù)SKIPIF1<0與SKIPIF1<0SKIPIF1<0的圖象關(guān)于直線SKIPIF1<0對(duì)稱．（3）若SKIPIF1<0，對(duì)任意SKIPIF1<0SKIPIF1<0恒成立，則SKIPIF1<0的圖象關(guān)于直線SKIPIF1<0對(duì)稱．（4）函數(shù)SKIPIF1<0與函數(shù)SKIPIF1<0的圖象關(guān)于直線SKIPIF1<0對(duì)稱．（5）函數(shù)..SKIPIF1<0..與函數(shù)SKIPIF1<0的圖象關(guān)于直線SKIPIF1<0對(duì)稱．（6）函數(shù)SKIPIF1<0與函數(shù)SKIPIF1<0的圖象關(guān)于點(diǎn)SKIPIF1<0中心對(duì)稱．（7）函數(shù)平移遵循自變量“左加右減”，函數(shù)值“上加下減”．題型一：由解析式選圖（識(shí)圖）【例1】（2023·山東煙臺(tái)·統(tǒng)考二模）函數(shù)SKIPIF1<0的部分圖象大致為（

）A． B．C． D．【對(duì)點(diǎn)訓(xùn)練1】（2023·重慶·統(tǒng)考模擬預(yù)測(cè)）函數(shù)SKIPIF1<0的圖像是（

）A．

B．

C．

D．

【對(duì)點(diǎn)訓(xùn)練2】（2023·安徽安慶·安慶市第二中學(xué)?？级＃┖瘮?shù)SKIPIF1<0的部分圖象大致是（

）A． B．C． D．【對(duì)點(diǎn)訓(xùn)練3】（2023·全國(guó)·模擬預(yù)測(cè)）函數(shù)SKIPIF1<0的大致圖像為（

）A．

B．

C．

D．

【解題方法總結(jié)】利用函數(shù)的性質(zhì)（如定義域、值域、奇偶性、單調(diào)性、周期性、特殊點(diǎn)等）排除錯(cuò)誤選項(xiàng)，從而篩選出正確答案題型二：由圖象選表達(dá)式【例2】（2023·四川遂寧·統(tǒng)考二模）數(shù)學(xué)與音樂有著緊密的關(guān)聯(lián)，我們平時(shí)聽到的樂音一般來說并不是純音，而是由多種波疊加而成的復(fù)合音．如圖為某段樂音的圖像，則該段樂音對(duì)應(yīng)的函數(shù)解析式可以為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0【對(duì)點(diǎn)訓(xùn)練4】（2023·全國(guó)·校聯(lián)考模擬預(yù)測(cè)）已知函數(shù)SKIPIF1<0在SKIPIF1<0上的圖像如圖所示，則SKIPIF1<0的解析式可能是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0【對(duì)點(diǎn)訓(xùn)練5】（2023·河北·統(tǒng)考模擬預(yù)測(cè)）已知函數(shù)SKIPIF1<0的部分圖象如圖所示，則SKIPIF1<0的解析式可能為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0【對(duì)點(diǎn)訓(xùn)練6】（2023·貴州遵義·?？寄M預(yù)測(cè)）已知函數(shù)SKIPIF1<0在SKIPIF1<0上的大致圖象如下所示，則SKIPIF1<0的解析式可能為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0【解題方法總結(jié)】1、從定義域值域判斷圖像位置；2、從奇偶性判斷對(duì)稱性；3、從周期性判斷循環(huán)往復(fù)；4、從單調(diào)性判斷變化趨勢(shì)；5、從特征點(diǎn)排除錯(cuò)誤選項(xiàng)．題型三：表達(dá)式含參數(shù)的圖象問題【例3】（2023·全國(guó)·高三專題練習(xí)）在同一直角坐標(biāo)系中，函數(shù)SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0的圖象可能是（

）A． B．C． D．【對(duì)點(diǎn)訓(xùn)練7】（2023·山東濱州·統(tǒng)考二模）函數(shù)SKIPIF1<0的圖象如圖所示，則（

）A．SKIPIF1<0，SKIPIF1<0，SKIPIF1<0 B．SKIPIF1<0，SKIPIF1<0，SKIPIF1<0C．SKIPIF1<0，SKIPIF1<0，SKIPIF1<0 D．SKIPIF1<0，SKIPIF1<0，SKIPIF1<0【對(duì)點(diǎn)訓(xùn)練8】（2023·全國(guó)·高三專題練習(xí)）已知函數(shù)SKIPIF1<0（a，b為常數(shù)，其中SKIPIF1<0且SKIPIF1<0）的圖象如圖所示，則下列結(jié)論正確的是（

）A．SKIPIF1<0，SKIPIF1<0 B．SKIPIF1<0，SKIPIF1<0C．SKIPIF1<0，SKIPIF1<0 D．SKIPIF1<0，SKIPIF1<0【對(duì)點(diǎn)訓(xùn)練9】（2023·全國(guó)·高三專題練習(xí)）若函數(shù)SKIPIF1<0的部分圖象如圖所示，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【對(duì)點(diǎn)訓(xùn)練10】（2023·全國(guó)·高三專題練習(xí)）在同一直角坐標(biāo)系中，函數(shù)SKIPIF1<0且SKIPIF1<0的圖象可能是A． B．C． D．【對(duì)點(diǎn)訓(xùn)練11】（多選題）（2023·全國(guó)·高三專題練習(xí)）函數(shù)SKIPIF1<0在SKIPIF1<0,SKIPIF1<0上的大致圖像可能為（）A． B．C． D．【解題方法總結(jié)】根據(jù)函數(shù)的解析式識(shí)別函數(shù)的圖象，其中解答中熟記指數(shù)冪的運(yùn)算性質(zhì)，二次函數(shù)的圖象與性質(zhì)，以及復(fù)合函數(shù)的單調(diào)性的判定方法是解答的關(guān)鍵，著重考查分析問題和解答問題的能力，以及分類討論思想的應(yīng)用．題型四：函數(shù)圖象應(yīng)用題【例4】（2023·北京·高三專題練習(xí)）高為SKIPIF1<0、滿缸水量為SKIPIF1<0的魚缸的軸截面如圖所示，現(xiàn)底部有一個(gè)小洞，滿缸水從洞中流出，若魚缸水深為SKIPIF1<0時(shí)水的體積為SKIPIF1<0，則函數(shù)SKIPIF1<0的大致圖像是A． B．C． D．【對(duì)點(diǎn)訓(xùn)練12】（2023·四川成都·高三四川省成都市玉林中學(xué)?？茧A段練習(xí)）如圖為某無人機(jī)飛行時(shí)，從某時(shí)刻開始15分鐘內(nèi)的速度SKIPIF1<0（單位：米/分鐘）與時(shí)間SKIPIF1<0（單位：分鐘）的關(guān)系．若定義“速度差函數(shù)”SKIPIF1<0為無人機(jī)在時(shí)間段SKIPIF1<0內(nèi)的最大速度與最小速度的差，則SKIPIF1<0的圖像為（

）A． B．C． D．【對(duì)點(diǎn)訓(xùn)練13】（2023·湖南長(zhǎng)沙·高三長(zhǎng)沙一中校考階段練習(xí)）青花瓷，又稱白地青花瓷，常簡(jiǎn)稱青花，是中國(guó)瓷器的主流品種之一.如圖，這是景德鎮(zhèn)青花瓷，現(xiàn)往該青花瓷中勻速注水，則水的高度SKIPIF1<0與時(shí)間SKIPIF1<0的函數(shù)圖像大致是（

）A． B．C． D．【對(duì)點(diǎn)訓(xùn)練14】（2023·全國(guó)·高三專題練習(xí)）列車從SKIPIF1<0地出發(fā)直達(dá)SKIPIF1<0外的SKIPIF1<0地，途中要經(jīng)過離SKIPIF1<0地SKIPIF1<0的SKIPIF1<0地，假設(shè)列車勻速前進(jìn)，SKIPIF1<0后從SKIPIF1<0地到達(dá)SKIPIF1<0地，則列車與SKIPIF1<0地距離SKIPIF1<0（單位：SKIPIF1<0與行駛時(shí)間SKIPIF1<0（單位：SKIPIF1<0）的函數(shù)圖象為（

）A． B．C． D．【對(duì)點(diǎn)訓(xùn)練15】（2023·全國(guó)·高三專題練習(xí)）如圖，正△ABC的邊長(zhǎng)為2，點(diǎn)D為邊AB的中點(diǎn)，點(diǎn)P沿著邊AC，CB運(yùn)動(dòng)到點(diǎn)B，記∠ADP＝x．函數(shù)f（x）＝|PB|2﹣|PA|2，則y＝f（x）的圖象大致為（）A． B．C． D．【對(duì)點(diǎn)訓(xùn)練16】（2023·全國(guó)·高三專題練習(xí)）勻速地向一底面朝上的圓錐形容器注水，則該容器盛水的高度h關(guān)于注水時(shí)間t的函數(shù)圖象大致是（

）A． B．C． D．【解題方法總結(jié)】（1）從函數(shù)的定義域，判斷圖象的左右位置；從函數(shù)的值域，判斷圖象的上下位置．（2）從函數(shù)的單調(diào)性，判斷圖象的變化趨勢(shì)；（3）從函數(shù)的奇偶性，判斷圖象的對(duì)稱性；（4）從函數(shù)的特征點(diǎn)，排除不合要求的圖象．題型五：函數(shù)圖象的變換【例5】（2023·廣西玉林·統(tǒng)考模擬預(yù)測(cè)）已知圖1對(duì)應(yīng)的函數(shù)為SKIPIF1<0，則圖2對(duì)應(yīng)的函數(shù)是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【對(duì)點(diǎn)訓(xùn)練17】（2023·全國(guó)·高三專題練習(xí)）已知函數(shù)SKIPIF1<0的圖象的一部分如下左圖，則如下右圖的函數(shù)圖象所對(duì)應(yīng)的函數(shù)解析式（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0【對(duì)點(diǎn)訓(xùn)練18】（2023·全國(guó)·高三專題練習(xí)）已知函數(shù)SKIPIF1<0，則下列圖象錯(cuò)誤的是（

）A． B．C． D．【對(duì)點(diǎn)訓(xùn)練19】（2023·全國(guó)·高三專題練習(xí)）函數(shù)SKIPIF1<0向右平移1個(gè)單位，再向上平移2個(gè)單位的大致圖像為()A． B．C． D．【解題方法總結(jié)】熟悉函數(shù)三種變換：（1）平移變換；（2）對(duì)稱變換；（3）伸縮變換.題型六：函數(shù)圖像的綜合應(yīng)用【例6】（2023·上海浦東新·華師大二附中?？寄M預(yù)測(cè)）若關(guān)于SKIPIF1<0的方程SKIPIF1<0恰有兩個(gè)不同的實(shí)數(shù)解，則實(shí)數(shù)SKIPIF1<0__________.【對(duì)點(diǎn)訓(xùn)練20】（2023·天津和平·統(tǒng)考三模）已知函數(shù)SKIPIF1<0，若關(guān)于SKIPIF1<0的方程SKIPIF1<0恰有三個(gè)不相等的實(shí)數(shù)解，則實(shí)數(shù)SKIPIF1<