第21講函數(shù)y＝Asin(ωx＋φ)的圖象性質(zhì)及其應(yīng)用（精講）題型目錄一覽①函數(shù)y＝Asin(ωx＋φ)的單調(diào)性②函數(shù)y＝Asin(ωx＋φ)的奇偶性、對稱性③函數(shù)y＝Asin(ωx＋φ)的圖像變換④根據(jù)圖像求函數(shù)y＝Asin(ωx＋φ)的解析式⑤三角函數(shù)圖像與性質(zhì)的綜合應(yīng)用一、知識點梳理一、知識點梳理一、SKIPIF1<0的圖像與性質(zhì)（1）最小正周期：SKIPIF1<0.（2）定義域與值域：SKIPIF1<0的定義域為R，值域為[-A,A].（3）最值（以下SKIPIF1<0）SKIPIF1<0（4）單調(diào)性SKIPIF1<0（5）對稱軸與對稱中心.SKIPIF1<0正弦曲線的對稱軸是相應(yīng)函數(shù)取最大（?。┲档奈恢?，對稱中心是與SKIPIF1<0軸交點的位置.（6）平移與伸縮函數(shù)y＝sinx的圖象變換得到y(tǒng)＝Asin(ωx＋φ)(ω>0)的圖象的步驟注：每一個變換總是對變量SKIPIF1<0而言的，即圖像變換要看“變量SKIPIF1<0”發(fā)生多大變化，而不是“角SKIPIF1<0”變化多少.【常用結(jié)論】1.根據(jù)圖像求解析式一般步驟①根據(jù)最高最低點求出A②根據(jù)周期算出SKIPIF1<0,題目一般會提供周期的一部分③通過帶最高或最低點算出φ2.對稱與周期(1)y＝Asin(ωx＋φ)相鄰兩條對稱軸之間的距離是SKIPIF1<0；(2)y＝Asin(ωx＋φ)相鄰兩個對稱中心的距離是SKIPIF1<0；(3)y＝Asin(ωx＋φ)相鄰兩條對稱軸與對稱中心距離SKIPIF1<0；3.函數(shù)具有奇、偶性的充要條件(1)函數(shù)y＝Asin(ωx＋φ)(x∈R)是奇函數(shù)?φ＝kπ(k∈Z)；(2)函數(shù)y＝Asin(ωx＋φ)(x∈R)是偶函數(shù)?φ＝kπ＋eq\f(π,2)(k∈Z)；(3)函數(shù)y＝Acos(ωx＋φ)(x∈R)是奇函數(shù)?φ＝kπ＋eq\f(π,2)(k∈Z)；(4)函數(shù)y＝Acos(ωx＋φ)(x∈R)是偶函數(shù)?φ＝kπ(k∈Z)．二、題型分類精講二、題型分類精講題型一函數(shù)y＝Asin(ωx＋φ)的單調(diào)性【典例1】函數(shù)SKIPIF1<0的單調(diào)遞增區(qū)間是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【題型訓(xùn)練】一、單選題1．已知函數(shù)SKIPIF1<0，則（

）A．SKIPIF1<0在SKIPIF1<0上單調(diào)遞減 B．SKIPIF1<0在SKIPIF1<0上單調(diào)遞增C．SKIPIF1<0在SKIPIF1<0上單調(diào)遞減 D．SKIPIF1<0在SKIPIF1<0上單調(diào)遞增2．下列區(qū)間中，函數(shù)SKIPIF1<0單調(diào)遞減的區(qū)間是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．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<04．下列不等式成立的是（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0二、多選題5．已知函數(shù)SKIPIF1<0，則（

）A．SKIPIF1<0的最小正周期為SKIPIF1<0 B．SKIPIF1<0在SKIPIF1<0上單調(diào)遞增C．SKIPIF1<0的圖象關(guān)于直線SKIPIF1<0對稱 D．若SKIPIF1<0，則SKIPIF1<0的最小值為SKIPIF1<06．關(guān)于函數(shù)SKIPIF1<0，下列說法正確的是（

）A．函數(shù)SKIPIF1<0在SKIPIF1<0上最大值為SKIPIF1<0 B．函數(shù)SKIPIF1<0的圖象關(guān)于點SKIPIF1<0對稱C．函數(shù)SKIPIF1<0在SKIPIF1<0上單調(diào)遞增 D．函數(shù)SKIPIF1<0的最小正周期為SKIPIF1<07．設(shè)函數(shù)SKIPIF1<0，則（

）A．SKIPIF1<0是偶函數(shù) B．SKIPIF1<0在SKIPIF1<0上單調(diào)遞減C．SKIPIF1<0的最大值為2 D．SKIPIF1<0的圖象關(guān)于直線SKIPIF1<0對稱三、填空題8．函數(shù)SKIPIF1<0的遞增區(qū)間為___________.9．函數(shù)SKIPIF1<0的單調(diào)遞減區(qū)間為______.10．已知函數(shù)SKIPIF1<0，SKIPIF1<0.則SKIPIF1<0的最大值為___________.11．函數(shù)SKIPIF1<0的單調(diào)增區(qū)間是______．12．請寫出一個滿足下列3個條件的函數(shù)SKIPIF1<0的表達式__________.①SKIPIF1<0；②在SKIPIF1<0上單調(diào)遞減；③SKIPIF1<0.四、解答題13．已知函數(shù)SKIPIF1<0，再從①SKIPIF1<0的最大值與最小值之和為0，②SKIPIF1<0這兩個條件中選擇一個作為已知條件.(1)求m的值；(2)求函數(shù)SKIPIF1<0在SKIPIF1<0上的單調(diào)遞增區(qū)間.注：如果選擇條件①和條件②分別解答，按第一個解答計分.14．已知函數(shù)SKIPIF1<0．(1)求函數(shù)SKIPIF1<0的周期及在SKIPIF1<0上的單調(diào)遞增區(qū)間：(2)若關(guān)于SKIPIF1<0的方程SKIPIF1<0在SKIPIF1<0上有兩個不同的實數(shù)根．求實數(shù)SKIPIF1<0的取值范圍．題型二函數(shù)y＝Asin(ωx＋φ)的奇偶性、對稱性【典例1】使函數(shù)SKIPIF1<0為偶函數(shù)的最小正數(shù)φ＝（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【典例2】已知函數(shù)SKIPIF1<0，則下列說法正確的是（

）A．SKIPIF1<0的最小正周期是SKIPIF1<0 B．SKIPIF1<0的最大值是SKIPIF1<0C．SKIPIF1<0的圖象的一條對稱軸是直線SKIPIF1<0 D．SKIPIF1<0的圖象的一個對稱中心是SKIPIF1<0【題型訓(xùn)練】一、單選題1．使函數(shù)SKIPIF1<0為偶函數(shù)，則SKIPIF1<0的一個值可以是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．已知函數(shù)SKIPIF1<0，若SKIPIF1<0是函數(shù)SKIPIF1<0圖象的一條對稱軸，則其圖象的一個對稱中心為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．已知曲線SKIPIF1<0的一條對稱軸是SKIPIF1<0，則SKIPIF1<0的值可能為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．已知函數(shù)SKIPIF1<0的最小正周期為T，且SKIPIF1<0，若SKIPIF1<0的圖象關(guān)于直線SKIPIF1<0對稱，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．函數(shù)SKIPIF1<0的圖像向左平移SKIPIF1<0個單位得到函數(shù)SKIPIF1<0的圖像，若函數(shù)SKIPIF1<0是偶函數(shù)，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．已知函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0單調(diào)遞增，直線SKIPIF1<0和SKIPIF1<0為函數(shù)SKIPIF1<0的圖像的兩條對稱軸，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<07．已知函數(shù)SKIPIF1<0．則“SKIPIF1<0”是“SKIPIF1<0為偶函數(shù)”的（

）A．充分而不必要條件 B．必要而不充分條件C．充分必要條件 D．既不充分也不必要條件8．將函數(shù)SKIPIF1<0的圖象向右平移SKIPIF1<0個單位長度后的函數(shù)圖象關(guān)于原點對稱，則實數(shù)SKIPIF1<0的最小值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<09．已知函數(shù)SKIPIF1<0圖象的一個對稱中心是SKIPIF1<0，點SKIPIF1<0在SKIPIF1<0的圖象上，下列說法錯誤的是（

）A．SKIPIF1<0 B．直線SKIPIF1<0是SKIPIF1<0圖象的一條對稱軸C．SKIPIF1<0在SKIPIF1<0上單調(diào)遞減 D．SKIPIF1<0是奇函數(shù)10．已知函數(shù)SKIPIF1<0圖象的兩個相鄰零點的差的絕對值為SKIPIF1<0，則（

）A．SKIPIF1<0的最小正周期為SKIPIF1<0B．將SKIPIF1<0的圖象向左平移SKIPIF1<0個單位長度，得到函數(shù)SKIPIF1<0的圖象C．SKIPIF1<0的圖象關(guān)于直線SKIPIF1<0對稱D．SKIPIF1<0的單調(diào)遞增區(qū)間為SKIPIF1<0二、多選題11．設(shè)函數(shù)SKIPIF1<0，若函數(shù)SKIPIF1<0為偶函數(shù)，則SKIPIF1<0的值可以是（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<012．若函數(shù)SKIPIF1<0的圖象關(guān)于坐標(biāo)原點對稱，則SKIPIF1<0的可能取值為（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<013．關(guān)于函數(shù)SKIPIF1<0，下列結(jié)論正確的是（

）A．函數(shù)SKIPIF1<0的周期為SKIPIF1<0 B．函數(shù)SKIPIF1<0圖象關(guān)于直線SKIPIF1<0對稱C．函數(shù)SKIPIF1<0在SKIPIF1<0上遞增 D．函數(shù)SKIPIF1<0的最大值為114．已知函數(shù)SKIPIF1<0的圖象關(guān)于點SKIPIF1<0中心對稱，則（

）A．SKIPIF1<0在區(qū)間SKIPIF1<0單調(diào)遞減 B．SKIPIF1<0在區(qū)間SKIPIF1<0有兩個極值點C．直線SKIPIF1<0是曲線SKIPIF1<0的對稱軸 D．直線SKIPIF1<0是曲線SKIPIF1<0的切線三、填空題15．設(shè)函數(shù)SKIPIF1<0的圖象關(guān)于點SKIPIF1<0成中心對稱，若SKIPIF1<0，則SKIPIF1<0______.16．已知函數(shù)SKIPIF1<0圖象關(guān)于直線SKIPIF1<0對稱，則函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上零點的個數(shù)為_______.17．某函數(shù)SKIPIF1<0滿足以下三個條件：①SKIPIF1<0是偶函數(shù)；②SKIPIF1<0；③SKIPIF1<0的最大值為4．請寫出一個滿足上述條件的函數(shù)SKIPIF1<0的解析式______．18．已知函數(shù)SKIPIF1<0的最小正周期為π，對于下列說法:①SKIPIF1<0;

②SKIPIF1<0的單調(diào)遞增區(qū)間為SKIPIF1<0，（SKIPIF1<0）;③將SKIPIF1<0的圖象向左平移SKIPIF1<0個單位長度后所得圖象關(guān)于y軸對稱;④SKIPIF1<0.其中正確的序號是__________.四、解答題19．已知函數(shù)SKIPIF1<0，SKIPIF1<0．（1）設(shè)SKIPIF1<0是函數(shù)SKIPIF1<0圖象的一條對稱軸，求SKIPIF1<0的值．（2）求函數(shù)SKIPIF1<0的單調(diào)遞增區(qū)間．20．已知函數(shù)SKIPIF1<0，SKIPIF1<0．(1)求SKIPIF1<0的對稱軸；(2)若SKIPIF1<0在SKIPIF1<0內(nèi)的最大值與最小值之和為SKIPIF1<0，求a．題型三函數(shù)y＝Asin(ωx＋φ)的圖像變換策略方法(1)變換前后，函數(shù)的名稱要一致，若不一致，應(yīng)先利用誘導(dǎo)公式轉(zhuǎn)化為同名函數(shù)；(2)要弄清變換的方向，即變換的是哪個函數(shù)的圖象，得到的是哪個函數(shù)的圖象，切不可弄錯方向；(3)要弄準(zhǔn)變換量的大小，特別是平移變換中，函數(shù)y＝Asinx到y(tǒng)＝Asin(x＋φ)的變換量是|φ|個單位，而函數(shù)y＝Asinωx到y(tǒng)＝Asin(ωx＋φ)時，變換量是eq\b\lc\|\rc\|(\a\vs4\al\co1(\f(φ,ω)))個單位．【典例1】為得到函數(shù)SKIPIF1<0的圖象，只需把函數(shù)SKIPIF1<0圖象上的所有點的（

）A．橫坐標(biāo)伸長到原來的2倍，縱坐標(biāo)不變，再把得到的圖象向左平移SKIPIF1<0個單位長度B．橫坐標(biāo)伸長到原來的2倍，縱坐標(biāo)不變，再把得到的圖象向右平移SKIPIF1<0個單位長度C．橫坐標(biāo)縮短到原來的SKIPIF1<0，縱坐標(biāo)不變，再把得到的圖象向左平移SKIPIF1<0個單位長度D．橫坐標(biāo)縮短到原來的SKIPIF1<0，縱坐標(biāo)不變，再把得到的圖象向右平移SKIPIF1<0個單位長度【題型訓(xùn)練】一、單選題1．把函數(shù)SKIPIF1<0圖象上所有點的縱坐標(biāo)不變，橫坐標(biāo)伸長到原來的2倍，再把所得曲線向右平移SKIPIF1<0個單位長度，得到函數(shù)SKIPIF1<0的圖象，則SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<02．將函數(shù)SKIPIF1<0的圖象上各點向右平移SKIPIF1<0個單位長度得函數(shù)SKIPIF1<0的圖象，則SKIPIF1<0的單調(diào)遞增區(qū)間為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．將函數(shù)SKIPIF1<0的圖象向右平移SKIPIF1<0個單位長度，再把所得圖象各點的橫坐標(biāo)縮小到原來的SKIPIF1<0（縱坐標(biāo)不變），所得圖象的一條對稱軸為SKIPIF1<0（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．將函數(shù)SKIPIF1<0的圖象向右平移SKIPIF1<0個單位長度，所得圖象對應(yīng)的函數(shù)（

）A．在區(qū)間SKIPIF1<0上單調(diào)遞增 B．在區(qū)間SKIPIF1<0上單調(diào)遞減C．在區(qū)間SKIPIF1<0上單調(diào)遞增 D．在區(qū)間SKIPIF1<0上單調(diào)遞減5．已知曲線SKIPIF1<0，則下面結(jié)論正確的是（

）A．把C1上各點的橫坐標(biāo)伸長到原來的SKIPIF1<0倍，縱坐標(biāo)不變，再把得到的曲線向右平移SKIPIF1<0個單位長度，得到曲線C2B．把C1上各點的橫坐標(biāo)伸長到原來的SKIPIF1<0倍，縱坐標(biāo)不變，再把得到的曲線向左平移SKIPIF1<0個單位長度，得到曲線C2C．把C1上各點的橫坐標(biāo)縮短到原來的SKIPIF1<0，縱坐標(biāo)不變，再把得到的曲線向左平移SKIPIF1<0個單位長度C2D．把C1上各點的橫坐標(biāo)縮短到原來的SKIPIF1<0，縱坐標(biāo)不變，再把得到的曲線向右平移SKIPIF1<0個單位長度，得到曲線C26．將函數(shù)SKIPIF1<0的圖象向右平移SKIPIF1<0個單位得到函數(shù)SKIPIF1<0的圖象，則“SKIPIF1<0”是“函數(shù)SKIPIF1<0為偶函數(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7．設(shè)函數(shù)SKIPIF1<0SKIPIF1<0，將函數(shù)SKIPIF1<0的圖象先向右平移SKIPIF1<0個單位長度，再將橫坐標(biāo)伸長到原來的2倍，縱坐標(biāo)不變，所得的圖象與SKIPIF1<0圖象重合，則（

）A．SKIPIF1<0，SKIPIF1<0 B．SKIPIF1<0，SKIPIF1<0C．SKIPIF1<0，SKIPIF1<0 D．SKIPIF1<0，SKIPIF1<0二、多選題8．將函數(shù)SKIPIF1<0的圖象向右平移SKIPIF1<0個單位長度得到函數(shù)SKIPIF1<0的圖象.則下列關(guān)于SKIPIF1<0的說法錯誤的是（

）A．最小正周期為SKIPIF1<0 B．圖象關(guān)于點SKIPIF1<0對稱C．在區(qū)間SKIPIF1<0上單調(diào)遞增 D．圖象關(guān)于直線SKIPIF1<0對稱9．已知函數(shù)SKIPIF1<0的圖象向左平移SKIPIF1<0）個單位長度后對應(yīng)的函數(shù)為SKIPIF1<0，若SKIPIF1<0在SKIPIF1<0上單調(diào)，則SKIPIF1<0的可取（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<010．已知函數(shù)SKIPIF1<0圖像的一條對稱軸為SKIPIF1<0，先將函數(shù)SKIPIF1<0的圖像上所有點的橫坐標(biāo)伸長為原來的3倍，再將所得圖像上所有的點向右平移SKIPIF1<0個單位長度，得到函數(shù)SKIPIF1<0的圖像，則函數(shù)SKIPIF1<0的圖像在以下哪些區(qū)間上單調(diào)遞減（

）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0三、填空題11．已知SKIPIF1<0，函數(shù)SKIPIF1<0，SKIPIF1<0的最小正周期為SKIPIF1<0，將SKIPIF1<0的圖像向左平移SKIPIF1<0個單位長度，所得圖像關(guān)于SKIPIF1<0軸對稱，則SKIPIF1<0的值是______．12．已知函數(shù)SKIPIF1<0，把SKIPIF1<0的圖象向右平移SKIPIF1<0個單位長度，得到函數(shù)SKIPIF1<0的圖象，則SKIPIF1<0________．四、解答題13．將函數(shù)SKIPIF1<0的圖象先向右平移SKIPIF1<0個單位長度，再將所得函圖象上所有點的橫坐標(biāo)變?yōu)樵瓉淼腟KIPIF1<0（ω＞0）倍（縱坐標(biāo)不變），得到函數(shù)SKIPIF1<0的圖象．(1)若SKIPIF1<0，求函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上的最大值；(2)若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上沒有零點，求ω的取值范圍．14．已知函數(shù)SKIPIF1<0的圖像相鄰對稱軸之間的距離是SKIPIF1<0，______；①若將SKIPIF1<0的圖像向右平移SKIPIF1<0個單位，所得函數(shù)SKIPIF1<0為奇函數(shù)．②若將SKIPIF1<0的圖像向左平移SKIPIF1<0個單位，所得函數(shù)SKIPIF1<0為偶函數(shù)，在①，②兩個條件中選擇一個補充在______并作答(1)若SKIPIF1<0，求SKIPIF1<0的取值范圍；(2)設(shè)函數(shù)SKIPIF1<0的零點為SKIPIF1<0，求SKIPIF1<0的值．題型四根據(jù)圖像求函數(shù)y＝Asin(ωx＋φ)的解析式策略方法確定y＝Asin(ωx＋φ)＋B(A＞0，ω＞0)的解析式的步驟(1)求A，B，確定函數(shù)的最大值M和最小值m，則A＝eq\f(M－m,2)，B＝eq\f(M＋m,2)．(2)求ω，確定函數(shù)的周期T，則ω＝eq\f(2π,T)．(3)求φ，常用方法為代入法，即把圖象上的一個已知點代入(此時要注意該點在上升區(qū)間上還是在下降區(qū)間上)或把圖象的最高點或最低點代入．【典例1】函數(shù)SKIPIF1<0（其中SKIPIF1<0，SKIPIF1<0，SKIPIF1<0）的圖象如圖所示，為得到SKIPIF1<0的圖象，只需將SKIPIF1<0圖象上所有的點（

）A．向左平移SKIPIF1<0個單位長度 B．向右平移SKIPIF1<0個單位長度C．向左平移SKIPIF1<0個單位長度 D．向右平移SKIPIF1<0個單位長度【題型訓(xùn)練】一、單選題1．已知函數(shù)SKIPIF1<0的部分圖象如圖所示，將函數(shù)SKIPIF1<0圖象上所有的點向左平移SKIPIF1<0個單位長度得到函數(shù)SKIPIF1<0的圖象，則SKIPIF1<0的值為（

）

A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<02．已知SKIPIF1<0的部分圖象如圖所示，則SKIPIF1<0的解析式為（

）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<03．函數(shù)SKIPIF1<0的部分圖象如圖所示，將函數(shù)SKIPIF1<0圖象上所有點的橫坐標(biāo)變?yōu)樵瓉淼腟KIPIF1<0（縱坐標(biāo)不變），再向左平移SKIPIF1<0個單位得到SKIPIF1<0的圖象，則下列說法不正確的是（

）A．函數(shù)SKIPIF1<0的最小正周期為SKIPIF1<0 B．函數(shù)SKIPIF1<0在SKIPIF1<0上單調(diào)遞增C．函數(shù)SKIPIF1<0的一個極值點為SKIPIF1<0 D．函數(shù)SKIPIF1<0的一個零點為SKIPIF1<04．已知函數(shù)SKIPIF1<0的部分圖象如圖所示，則下列說法正確的是（

）

A．SKIPIF1<0的最小值是SKIPIF1<0B．SKIPIF1<0的最小正周期為SKIPIF1<0C．SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞增D．將SKIPIF1<0的圖象向右平移SKIPIF1<0個單位長度后得到函數(shù)SKIPIF1<0的圖象5．已知函數(shù)SKIPIF1<0（SKIPIF1<0，SKIPIF1<0，SKIPIF1<0）的部分圖象如圖所示，關(guān)于該函數(shù)有下列四個說法：①SKIPIF1<0的圖象關(guān)于點SKIPIF1<0對稱；②SKIPIF1<0的圖象關(guān)于直線SKIPIF1<0對稱；③SKIPIF1<0的圖象可由SKIPIF1<0的圖象向左平移SKIPIF1<0個單位長度得到；⑧若方程SKIPIF1<0在SKIPIF1<0上有且只有兩個極值點，則SKIPIF1<0的最大值為SKIPIF1<0．以上四個說法中，正確的個數(shù)為（

）A．1 B．2 C．3 D．4二、多選題6．已知函數(shù)SKIPIF1<0的部分圖象如圖所示，則下列結(jié)論中正確的是（

）

A．SKIPIF1<0B．SKIPIF1<0C．點SKIPIF1<0是SKIPIF1<0的一個對稱中心D．函數(shù)SKIPIF1<0的圖象向左平移SKIPIF1<0個單位得到的圖象關(guān)于SKIPIF1<0軸對稱7．函數(shù)SKIPIF1<0的部分圖象如圖所示，則下列結(jié)論正確的是（

）

A．SKIPIF1<0B．SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞減C．將SKIPIF1<0的圖象向左平移SKIPIF1<0個單位所得函數(shù)為奇函數(shù)D．方程SKIPIF1<0在區(qū)間SKIPIF1<0內(nèi)有4個根三、填空題8．已知函數(shù)SKIPIF1<0的部分圖象如圖所示，將函數(shù)SKIPIF1<0圖象上所有的點向左平移SKIPIF1<0個單位長度得到函數(shù)SKIPIF1<0的圖象，則SKIPIF1<0的值為______.9．已知函數(shù)SKIPIF1<0的部分圖象如圖，SKIPIF1<0，則SKIPIF1<0____________．10．已知函數(shù)SKIPIF1<0的圖象如圖所示，且SKIPIF1<0在SKIPIF1<0的圖象上，則SKIPIF1<0的值為__________．

四、解答題11．已知函數(shù)SKIPIF1<0（SKIPIF1<0，SKIPIF1<0，SKIPIF1<0）的部分圖象如圖所示．

(1)求SKIPIF1<0的解析式；(2)設(shè)SKIPIF1<0，若函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上單調(diào)遞增，求實數(shù)SKIPIF1<0的最大值．12．已知函數(shù)SKIPIF1<0的部分圖象如圖所示.

(1)求函數(shù)SKIPIF1<0的解析式；(2)將函數(shù)SKIPIF1<0的圖象向左平移SKIPIF1<0個單位，得到函數(shù)SKIPIF1<0的圖象，若方程SKIPIF1<0在SKIPIF1<0上有解，求實數(shù)SKIPIF1<0的取值范圍.題型五三角函數(shù)圖像與性質(zhì)的綜合應(yīng)用策略方法由不等式恒成立求參數(shù)取值范圍的思路及關(guān)鍵解決三角函數(shù)圖象與性質(zhì)的綜合問題的關(guān)鍵是首先正確的將已知條件轉(zhuǎn)化為三角函數(shù)解析式和圖象，然后再根據(jù)數(shù)形結(jié)合思想研究函數(shù)的性質(zhì)(單調(diào)性、奇偶性、對稱性、周期性)，進而加深理解函數(shù)的極值點、最值點、零點及有界函數(shù)等概念．【典例1】已知向量SKIPIF1<0，SKIPIF1<0，函數(shù)SKIPIF1<0.(1)求SKIPIF1<0的單調(diào)增區(qū)間；(2)若函數(shù)SKIPIF1<0圖像上所有點的縱坐標(biāo)保持不變，橫坐標(biāo)變?yōu)樵瓉淼腟KIPIF1<0得函數(shù)SKIPIF1<0的圖像，且關(guān)于SKIPIF1<0的方程SKIPIF1<0在SKIPIF1<0上有解，求實數(shù)SKIPIF1<0的取值范圍.【題型訓(xùn)練】一、單選題1．已知函數(shù)SKIPIF1<0的圖象關(guān)于點SKIPIF1<0對稱，則（

）A．SKIPIF1<0在SKIPIF1<0單調(diào)遞增B．直線SKIPIF1<0是曲線SKIPIF1<