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第01講函數(shù)的概念及其表示(精講+精練)目錄第一部分:知識點精準(zhǔn)記憶第二部分:課前自我評估測試第三部分:典型例題剖析高頻考點一:函數(shù)的概念高頻考點二:函數(shù)定義域①具體函數(shù)的定義域;②抽象函數(shù)定義域高頻考點三:函數(shù)解析式①湊配法求解析式(注意定義域)②換元法求解析式(換元必?fù)Q范圍)③待定系數(shù)法;④方程組消去法高頻考點四:分段函數(shù)①分段函數(shù)求值②已知分段函數(shù)的值求參數(shù)③分段函數(shù)求值域(最值)高頻考點五:函數(shù)的值域①二次函數(shù)求值域;②分式型函數(shù)求值域③根式型函數(shù)求值域;④根據(jù)值域求參數(shù)⑤根據(jù)函數(shù)值域求定義域第四部分:高考真題感悟第五部分:第01講函數(shù)的概念及其表示(精練)第一部分:知識點精準(zhǔn)記憶第一部分:知識點精準(zhǔn)記憶1、函數(shù)的概念設(shè)SKIPIF1<0、SKIPIF1<0是兩個非空數(shù)集,如果按照某種確定的對應(yīng)關(guān)系SKIPIF1<0,使對于集合SKIPIF1<0中的任意一個數(shù)SKIPIF1<0,在集合SKIPIF1<0中都有唯一確定的數(shù)SKIPIF1<0和它對應(yīng),那么稱SKIPIF1<0為從集合SKIPIF1<0到集合SKIPIF1<0的一個函數(shù),記作SKIPIF1<0,SKIPIF1<0.其中:SKIPIF1<0叫做自變量,SKIPIF1<0的取值范圍SKIPIF1<0叫做函數(shù)的定義域與SKIPIF1<0的值相對應(yīng)的SKIPIF1<0值叫做函數(shù)值,函數(shù)值的集合SKIPIF1<0叫做函數(shù)的值域.2、同一(相等)函數(shù)函數(shù)的三要素:定義域、值域和對應(yīng)關(guān)系.同一(相等)函數(shù):如果兩個函數(shù)的定義和對應(yīng)關(guān)系完全一致,則這兩個函數(shù)相等,這是判斷兩函數(shù)相等的依據(jù).3、函數(shù)的表示函數(shù)的三種表示法解析法(最常用)圖象法(解題助手)列表法就是把變量SKIPIF1<0,SKIPIF1<0之間的關(guān)系用一個關(guān)系式SKIPIF1<0來表示,通過關(guān)系式可以由SKIPIF1<0的值求出SKIPIF1<0的值.就是把SKIPIF1<0,SKIPIF1<0之間的關(guān)系繪制成圖象,圖象上每個點的坐標(biāo)就是相應(yīng)的變量SKIPIF1<0,SKIPIF1<0的值.就是將變量SKIPIF1<0,SKIPIF1<0的取值列成表格,由表格直接反映出兩者的關(guān)系.4、分段函數(shù)若函數(shù)在其定義域內(nèi),對于定義域內(nèi)的不同取值區(qū)間,有著不同的對應(yīng)關(guān)系,這樣的函數(shù)通常叫做分段函數(shù).5、高頻考點結(jié)論5.1函數(shù)的定義域是使函數(shù)解析式有意義的自變量的取值范圍,常見基本初等函數(shù)定義域的要求為:(1)分式型函數(shù):分母不等于零.(2)偶次根型函數(shù):被開方數(shù)大于或等于0.(3)一次函數(shù)、二次函數(shù)的定義域均為SKIPIF1<0(4)SKIPIF1<0的定義域是SKIPIF1<0.(5)SKIPIF1<0(SKIPIF1<0且SKIPIF1<0),SKIPIF1<0,SKIPIF1<0的定義域均為SKIPIF1<0.(6)SKIPIF1<0(SKIPIF1<0且SKIPIF1<0)的定義域為SKIPIF1<0.(7)SKIPIF1<0的定義域為SKIPIF1<0.5.2函數(shù)求值域(1)分離常數(shù)法:將形如SKIPIF1<0(SKIPIF1<0)的函數(shù)分離常數(shù),變形過程為:SKIPIF1<0,再結(jié)合SKIPIF1<0的取值范圍確定SKIPIF1<0的取值范圍,從而確定函數(shù)的值域.(2)換元法:如:函數(shù)SKIPIF1<0,可以令SKIPIF1<0,得到SKIPIF1<0,函數(shù)SKIPIF1<0SKIPIF1<0可以化為SKIPIF1<0(SKIPIF1<0),接下來求解關(guān)于t的二次函數(shù)的值域問題,求解過程中要注意t的取值范圍的限制.(3)基本不等式法和對勾函數(shù)(4)單調(diào)性法(5)求導(dǎo)法第二部分:課前自我評估測試第二部分:課前自我評估測試一、判斷題1.(2021·江西·貴溪市實驗中學(xué)高二階段練習(xí))函數(shù)SKIPIF1<0和SKIPIF1<0是相同的函數(shù)()2.(2021·江西·貴溪市實驗中學(xué)高二階段練習(xí))函數(shù)SKIPIF1<0的定義域是SKIPIF1<0
()3.(2021·江西·貴溪市實驗中學(xué)高三階段練習(xí))已知SKIPIF1<0則SKIPIF1<0.()4.(2021·江西·貴溪市實驗中學(xué)高三階段練習(xí))函數(shù)SKIPIF1<0的定義域為SKIPIF1<0.()二、單選題1.(2022·寧夏·青銅峽市高級中學(xué)高二學(xué)業(yè)考試)如圖,可以表示函數(shù)SKIPIF1<0的圖象的是(
)A. B.C. D.2.(2022·全國·高一階段練習(xí))函數(shù)SKIPIF1<0的定義域為(
)A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<03.(2022·黑龍江·鐵人中學(xué)高一開學(xué)考試)以下各組函數(shù)中,表示同一函數(shù)的是(
)A.SKIPIF1<0,SKIPIF1<0 B.SKIPIF1<0,SKIPIF1<0C.SKIPIF1<0,SKIPIF1<0 D.SKIPIF1<0,SKIPIF1<04.(2022·安徽·北大培文蚌埠實驗學(xué)校高三開學(xué)考試(文))設(shè)函數(shù)SKIPIF1<0,若SKIPIF1<0(
)A.1 B.2 C.3 D.4第三部分:典型例題剖析第三部分:典型例題剖析高頻考點一:函數(shù)的概念1.(2022·全國·高三專題練習(xí))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.(2022·湖南·高一課時練習(xí))設(shè)集合SKIPIF1<0,SKIPIF1<0,那么下列四個圖形中,能表示集合SKIPIF1<0到集合SKIPIF1<0的函數(shù)關(guān)系的有(
)A.①②③④ B.①②③ C.②③ D.②3.(2022·江西贛州·高一期末)如圖所示某加油站地下圓柱體儲油罐示意圖,已知儲油罐長度為SKIPIF1<0,截面半徑為SKIPIF1<0(SKIPIF1<0,SKIPIF1<0為常量),油面高度為SKIPIF1<0,油面寬度為SKIPIF1<0,油量為SKIPIF1<0(SKIPIF1<0,SKIPIF1<0,SKIPIF1<0為變量),則下列說法錯誤的(
)A.SKIPIF1<0是SKIPIF1<0的函數(shù) B.SKIPIF1<0是SKIPIF1<0的函數(shù)C.SKIPIF1<0是SKIPIF1<0的函數(shù) D.SKIPIF1<0是SKIPIF1<0的函數(shù)4.(2022·江蘇泰州·高一期末)若函數(shù)SKIPIF1<0和SKIPIF1<0.分別由下表給出:SKIPIF1<0SKIPIF1<001SKIPIF1<010SKIPIF1<0SKIPIF1<0123SKIPIF1<001SKIPIF1<0則不等式SKIPIF1<0的解集為(
).A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<0高頻考點二:函數(shù)定義域①具體函數(shù)的定義域1.(2022·廣東汕尾·高一期末)函數(shù)SKIPIF1<0的定義域是(
)A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<02.(2022·湖北省廣水市實驗高級中學(xué)高一階段練習(xí))函數(shù)SKIPIF1<0的定義域為(
)A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<03.(2022·廣東潮州·高一期末)函數(shù)SKIPIF1<0的定義域為(
)A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<0②抽象函數(shù)定義域1.(2022·廣東·化州市第三中學(xué)高一階段練習(xí))已知函數(shù)y=f(x+1)定義域是[-2,3],則y=f(x-2)的定義域是()A.[1,6] B.[-1,4] C.[-3,2] D.[-2,3]2.(2022·重慶巴蜀中學(xué)高一期末)已知函數(shù)SKIPIF1<0的定義域為[1,10],則SKIPIF1<0的定義域為(
)A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<03.(2022·全國·高一)已知函數(shù)SKIPIF1<0的定義域為SKIPIF1<0,則函數(shù)SKIPIF1<0的定義域是(
)A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<0高頻考點三:函數(shù)解析式①湊配法求解析式(注意定義域)1.(2022·全國·高一)已知函數(shù)SKIPIF1<0,則SKIPIF1<0(
)A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<02.(2022·全國·高三專題練習(xí))已知SKIPIF1<0=SKIPIF1<0,則SKIPIF1<0的表達(dá)式是(
)A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<0②換元法求解析式(換元必?fù)Q范圍)1.(2022·全國·高三專題練習(xí))已知函數(shù)SKIPIF1<0,則SKIPIF1<0的解析式為(
)A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<02.(2022·浙江·高三專題練習(xí))已知SKIPIF1<0,則(
)A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<03.(2022·全國·高三專題練習(xí))若SKIPIF1<0,那么SKIPIF1<0等于(
)A.8 B.3 C.1 D.30③待定系數(shù)法1.(2022·全國·高三專題練習(xí))已知SKIPIF1<0是一次函數(shù),且SKIPIF1<0,則SKIPIF1<0的解析式為A.SKIPIF1<0或SKIPIF1<0 B.SKIPIF1<0或SKIPIF1<0C.SKIPIF1<0或SKIPIF1<0 D.SKIPIF1<0或SKIPIF1<02.(2022·湖南·高一課時練習(xí))已知二次函數(shù)f(x)的圖象經(jīng)過點(-3,2),頂點是(-2,3),則函數(shù)f(x)的解析式為___________.④方程組消去法1.(2022·全國·高三專題練習(xí))若函數(shù)SKIPIF1<0滿足SKIPIF1<0,則SKIPIF1<0(
)A.0 B.2 C.3 D.SKIPIF1<02.(2022·全國·高三專題練習(xí))已知函數(shù)SKIPIF1<0的定義域為SKIPIF1<0,且SKIPIF1<0,則SKIPIF1<0A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<03.(2022·全國·高三專題練習(xí))已知SKIPIF1<0滿足SKIPIF1<0,則SKIPIF1<0等于(
)A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<0高頻考點四:分段函數(shù)①分段函數(shù)求值1.(2022·甘肅張掖·高一期末)已知SKIPIF1<0,則SKIPIF1<0為(
)A.SKIPIF1<0 B.2 C.3 D.SKIPIF1<0或32.(2022·安徽阜陽·高一期中)函數(shù)SKIPIF1<0則SKIPIF1<0(
)A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<03.(2022·河南·高一階段練習(xí))若SKIPIF1<0是奇函數(shù),則SKIPIF1<0(
)A.2 B.SKIPIF1<0 C.3 D.54.(2022·黑龍江·牡丹江市第三高級中學(xué)高一開學(xué)考試)設(shè)SKIPIF1<0,則SKIPIF1<0的值為(
)A.0 B.1 C.2 D.3②已知分段函數(shù)的值求參數(shù)1.(2022·遼寧朝陽·高一開學(xué)考試)函數(shù)SKIPIF1<0,若SKIPIF1<0,則實數(shù)a的值為(
)A.±1 B.-2或±1 C.-1 D.-2或-12.(2022·新疆烏魯木齊·二模(理))已知函數(shù)SKIPIF1<0,若SKIPIF1<0,則SKIPIF1<0(
)A.SKIPIF1<0 B.2或SKIPIF1<0 C.SKIPIF1<0或2 D.SKIPIF1<0或SKIPIF1<03.(2022·江西南昌·一模(理))已知SKIPIF1<0若SKIPIF1<0,則SKIPIF1<0(
)A.2 B.SKIPIF1<0 C.1 D.04.(2022·河南洛陽·二模(文))已知函數(shù)SKIPIF1<0,且SKIPIF1<0,則SKIPIF1<0(
)A.26 B.16 C.-16 D.-26③分段函數(shù)求值域(最值)1.(2022·全國·高三專題練習(xí))SKIPIF1<0,若SKIPIF1<0是SKIPIF1<0的最小值,則SKIPIF1<0的取值范圍為(
).A.[SKIPIF1<01,2] B.[SKIPIF1<01,0] C.[1,2] D.SKIPIF1<02.(2022·江西·景德鎮(zhèn)一中高一期末)已知函數(shù)SKIPIF1<0的值域為SKIPIF1<0,那么實數(shù)SKIPIF1<0的取值范圍是(
)A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<03.(2022·全國·高三專題練習(xí))已知函數(shù)SKIPIF1<0的值域為R,則實數(shù)a的取值范圍是(
)A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<04.(2022·北京平谷·高一期末)已知函數(shù)SKIPIF1<0(1)求SKIPIF1<0,SKIPIF1<0的值;(2)作出函數(shù)的簡圖;(3)由簡圖指出函數(shù)的值域;5.(2022·湖南·高一課時練習(xí))已知函數(shù)f(x)=SKIPIF1<0求f(x)的最大值、最小值.高頻考點五:函數(shù)的值域①二次函數(shù)求值域1.(2022·黑龍江·哈爾濱市第三十二中學(xué)校高三期末(理))函數(shù)y=x2-2x+2在區(qū)間[-2,3]上的最大值、最小值分別是(
)A.10,5 B.10,1C.5,1 D.以上都不對2.(2022·全國·高三專題練習(xí))若函數(shù)SKIPIF1<0的定義域為SKIPIF1<0,值域為SKIPIF1<0,則SKIPIF1<0的取值范圍是(
)A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<03.(2022·全國·高三專題練習(xí))若函數(shù)SKIPIF1<0的定義域和值域都是SKIPIF1<0,則SKIPIF1<0(
)A.1 B.3 C.SKIPIF1<0 D.1或3②分式型函數(shù)求值域1.(2022·全國·江西科技學(xué)院附屬中學(xué)模擬預(yù)測(文))函數(shù)SKIPIF1<0的值域(
)A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<02.(2022·全國·高三專題練習(xí))函數(shù)SKIPIF1<0的值域是(
)A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<03.(2022·全國·高三專題練習(xí))函數(shù)SKIPIF1<0的值域為(
)A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<04.(2022·全國·高三專題練習(xí))函數(shù)SKIPIF1<0的值域為A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<05.(2022·全國·高三專題練習(xí))函數(shù)SKIPIF1<0的值域為________________.③根式型函數(shù)求值域1.(2022·全國·高三專題練習(xí))函數(shù)SKIPIF1<0的值域為(
)A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<02.(2022·全國·高三專題練習(xí))函數(shù)SKIPIF1<0的值域是(
)A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<03.(2022·全國·高三專題練習(xí))函數(shù)SKIPIF1<0的值域是(
)A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<04.(2022·全國·高二)函數(shù)SKIPIF1<0的值域是(
)A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<0④根據(jù)值域求參數(shù)1.(2022·全國·高三專題練習(xí))已知函數(shù)SKIPIF1<0的值域為SKIPIF1<0,求a的取值范圍為A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<02.(2022·全國·高三專題練習(xí))若函數(shù)SKIPIF1<0的定義域為SKIPIF1<0,值域為SKIPIF1<0,則SKIPIF1<0的取值范圍是(
)A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<03.(2022·全國·高三專題練習(xí))已知函數(shù)SKIPIF1<0的值域為SKIPIF1<0,則實數(shù)a的取值范圍是(
)A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<04.(2022·全國·高三專題練習(xí))已知函數(shù)SKIPIF1<0在SKIPIF1<0上的值域為SKIPIF1<0,則實數(shù)m的取值范圍是(
)A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<05.(2022·全國·高三專題練習(xí))已知二次函數(shù)SKIPIF1<0的值域為SKIPIF1<0,則SKIPIF1<0的最小值為(
)A.3 B.6 C.9 D.126.(2022·全國·高三專題練習(xí))已知函數(shù)SKIPIF1<0,SKIPIF1<0,若對任意SKIPIF1<0,總存在SKIPIF1<0,使得SKIPIF1<0,則實數(shù)a的取值范圍是(
)A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<0⑤根據(jù)函數(shù)值域求定義域1.(2021·山西·懷仁市第一中學(xué)校高一階段練習(xí))已知函數(shù)f(x)=x2-2x-3的定義域為[a,b],值域為[-4,5],則實數(shù)對(a,b)的不可能值為(
)A.(-2,4) B.(-2,1) C.(1,4) D.(-1,1)2.(2021·江蘇·高一專題練習(xí))若一系列函數(shù)的解析式相同,值域相同,但其定義域不同,則稱這些函數(shù)為“同族函數(shù)”.那么函數(shù)解析式為f(x)=x2,值域為{1,4}的“同族函數(shù)”共有(
)A.7個 B.8個 C.9個 D.無數(shù)個3.(2021·江西省泰和中學(xué)高二開學(xué)考試(理))定義區(qū)間SKIPIF1<0的長度為SKIPIF1<0,已知函數(shù)SKIPIF1<0的定義域為SKIPIF1<0,值域為SKIPIF1<0,則區(qū)間SKIPIF1<0的長度的最大值與最小值的差為(
)A.1 B.2 C.3 D.SKIPIF1<04.(2021·全國·高一課時練習(xí))已知函數(shù)SKIPIF1<0的值域為SKIPIF1<0,則函數(shù)SKIPIF1<0的定義域為______.第四部分:高考真題感悟第四部分:高考真題感悟1.(2021·山東·高考真題)函數(shù)SKIPIF1<0的定義域為(
)A.SKIPIF1<0且SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0且SKIPIF1<0 D.SKIPIF1<02.(2020·山東·高考真題)函數(shù)SKIPIF1<0的定義域是(
)A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<03.(2021·浙江·高考真題)已知SKIPIF1<0,函數(shù)SKIPIF1<0若SKIPIF1<0,則SKIPIF1<0___________.4.(2021·湖南·高考真題)已知函數(shù)SKIPIF1<0(1)畫出函數(shù)SKIPIF1<0的圖象;(2)若SKIPIF1<0,求SKIPIF1<0的取值范圍.5.(2020·山東·高考真題)已知函數(shù)SKIPIF1<0.(1)求SKIPIF1<0的值;(2)求SKIPIF1<0,求實數(shù)SKIPIF1<0的取值范圍.第五部分:第五部分:第01講函數(shù)的概念及其表示(精練)一、單選題1.(2022·全國·高一)已知SKIPIF1<0,SKIPIF1<0,下列圖形能表示以A為定義域,B為值域的函數(shù)的是(
)A. B.C. D.2.(2022·內(nèi)蒙古·赤峰紅旗中學(xué)松山分校高一期末(文))下列各組函數(shù)表示同一函數(shù)的是(
)A.SKIPIF1<0,SKIPIF1<0 B.SKIPIF1<0,SKIPIF1<0C.SKIPIF1<0,SKIPIF1<0 D.SKIPIF1<0,SKIPIF1<03.(2022·吉林·農(nóng)安縣教師進(jìn)修學(xué)校高一期末)函數(shù)SKIPIF1<0的定義域是(
)A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<04.(2022·全國·高三專題練習(xí)(理))若SKIPIF1<0,則SKIPIF1<0的解析式為(
)A.SKIPIF1<0 B.SKIPIF1<0C.SKIPIF1<0 D.SKIPIF1<05.(2022·四川成都·二模(文))已知函數(shù)SKIPIF1<0,則SKIPIF1<0(
)A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<06.(2022·遼寧朝陽·高一開學(xué)考試)若函數(shù)SKIPIF1<0在SKIPIF1<0上單調(diào)遞減,則實數(shù)SKIPIF1<0的取值范圍是(
)A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<07.(2022·全國·高一期末)某校要召開學(xué)生代表大會,規(guī)定各班每SKIPIF1<0人推選一名代表,當(dāng)班人數(shù)除以SKIPIF1<0的余數(shù)大于SKIPIF1<0時,再增選一名代表,則各班推選代表人數(shù)SKIPIF1<0與該班人數(shù)SKIPIF1<0之間的函數(shù)關(guān)系用取整函數(shù)SKIPIF1<0(SKIPIF1<0表示不大于SKIPIF1<0的最大整數(shù),如SKIPIF1<0,SKIPIF1<0)可表示為(
)A.SKIPIF1<0 B.SKIPIF1<0 C.SKIPIF1<0 D.SKIPIF1<08.(2022·內(nèi)蒙古·赤峰二中高一期末(理))設(shè)集合SKIPIF1<0,函數(shù)SKIPIF1<0,若SKIPIF1<0,且SKIPIF1<0,則SKIPIF1<0的取值范圍是(
)A.SKIPIF1<0
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