高考數(shù)學(xué)三輪沖刺壓軸小題02 辨析函數(shù)與方程的根的情況 (原卷版)

辨析函數(shù)與方程的根的情況一、方法綜述確定函數(shù)f(x)零點(diǎn)個數(shù)(方程f(x)＝0的實根個數(shù))的方法：(1)判斷二次函數(shù)f(x)在R上的零點(diǎn)個數(shù)，一般由對應(yīng)的二次方程f(x)＝0的判別式Δ＞0，Δ＝0，Δ＜0來完成；對于一些不便用判別式判斷零點(diǎn)個數(shù)的二次函數(shù)，則要結(jié)合二次函數(shù)的圖象進(jìn)行判斷．(2)對于一般函數(shù)零點(diǎn)個數(shù)的判斷，不僅要用到零點(diǎn)存在性定理，還必須結(jié)合函數(shù)的圖象和性質(zhì)才能確定，如三次函數(shù)的零點(diǎn)個數(shù)問題．(3)若函數(shù)f(x)在[a，b]上的圖象是連續(xù)不斷的一條曲線，且是單調(diào)函數(shù)，又f(a)·f(b)＜0，則y＝f(x)在區(qū)間(a，b)內(nèi)有唯一零點(diǎn)．二、解題策略類型一求方程解的個數(shù)例1．已知函數(shù)SKIPIF1<0函數(shù)SKIPIF1<0滿足以下三點(diǎn)條件：①定義域為SKIPIF1<0；②對任意SKIPIF1<0，有SKIPIF1<0；③當(dāng)SKIPIF1<0時，SKIPIF1<0．則函數(shù)SKIPIF1<0在區(qū)間SKIPIF1<0上零點(diǎn)的個數(shù)為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0【舉一反三】定義在R上的奇函數(shù)SKIPIF1<0滿足SKIPIF1<0，且當(dāng)SKIPIF1<0時，不等式SKIPIF1<0恒成立，則函數(shù)SKIPIF1<0的零點(diǎn)的個數(shù)為SKIPIF1<0SKIPIF1<0A．1 B．2 C．3 D．4熱點(diǎn)題型二已知方程的根求參數(shù)的值或取值范圍例2．已知函數(shù)SKIPIF1<0是定義在SKIPIF1<0上的偶函數(shù)，且滿足SKIPIF1<0，若函數(shù)SKIPIF1<0有6個零點(diǎn)，則實數(shù)SKIPIF1<0的取值范圍是A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<0【舉一反三】已知SKIPIF1<0，若函數(shù)SKIPIF1<0有三個零點(diǎn)，則實數(shù)SKIPIF1<0的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<0三、強(qiáng)化訓(xùn)練1．設(shè)函數(shù)是定義在R上的奇函數(shù)，當(dāng)時，則的零點(diǎn)個數(shù)為（）A．1B．2C．3D．42．若SKIPIF1<0圖象上存在兩點(diǎn)SKIPIF1<0，SKIPIF1<0關(guān)于原點(diǎn)對稱，則點(diǎn)對SKIPIF1<0稱為函數(shù)SKIPIF1<0的“友情點(diǎn)對”（點(diǎn)對SKIPIF1<0與SKIPIF1<0視為同一個“友情點(diǎn)對”）若SKIPIF1<0恰有兩個“友情點(diǎn)對”，則實數(shù)SKIPIF1<0的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<03．已知函數(shù)SKIPIF1<0，若關(guān)于SKIPIF1<0的方程SKIPIF1<0恰有兩個不等實根SKIPIF1<0，SKIPIF1<0，且SKIPIF1<0，則SKIPIF1<0的最小值為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<04．已知函數(shù)SKIPIF1<0，若關(guān)于x的方程SKIPIF1<0恰好有4個不相等的實根，則m取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<05．已知函數(shù)SKIPIF1<0有兩個零點(diǎn)SKIPIF1<0，且存在唯一的整數(shù)SKIPIF1<0，則實數(shù)SKIPIF1<0的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<06．已知SKIPIF1<0，設(shè)函數(shù)SKIPIF1<0，若關(guān)于SKIPIF1<0的方程SKIPIF1<0恰有兩個互異的實數(shù)解，則實數(shù)SKIPIF1<0的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<07．已知SKIPIF1<0.SKIPIF1<0是函數(shù)SKIPIF1<0(SKIPIF1<0)在SKIPIF1<0上的兩個零點(diǎn)，則SKIPIF1<0.SKIPIF1<0滿足（）A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<08．已知函數(shù)SKIPIF1<0是定義域為SKIPIF1<0的偶函數(shù)，當(dāng)SKIPIF1<0時，SKIPIF1<0，若關(guān)于SKIPIF1<0的方程SKIPIF1<0恰好有SKIPIF1<0個不同的實數(shù)根，那么SKIPIF1<0的值為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<09．已知函數(shù)SKIPIF1<0的圖像上相鄰的最高點(diǎn)和最低點(diǎn)之間的距離為SKIPIF1<0，關(guān)于SKIPIF1<0的方程SKIPIF1<0SKIPIF1<0在SKIPIF1<0上有兩個不同實根，則實數(shù)SKIPIF1<0的取值范圍是（）A．SKIPIF1<0B．SKIPIF1<0C．SKIPIF1<0D．SKIPIF1<010．已知函數(shù)SKIPIF1<0若關(guān)于SKIPIF1<0的方程SKIPIF1<0有6個根，則SKIPIF1<0的取值范圍為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<011．已知函數(shù)SKIPIF1<0，若關(guān)于SKIPIF1<0的方程SKIPIF1<0恰有兩個不同解SKIPIF1<0，則SKIPIF1<0的取值范圍是（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<012．已知SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，若函數(shù)SKIPIF1<0有且只有兩個零點(diǎn)，則實數(shù)k的取值范圍為（）A．SKIPIF1<0 B．SKIPIF1<0C．SKIPIF1<0 D．SKIPIF1<013．已知定義域為SKIPIF1<0的函數(shù)SKIPIF1<0的圖象關(guān)于SKIPIF1<0對稱，當(dāng)SKIPIF1<0時，SKIPIF1<0，若方程SKIPIF1<0有四個不等實根SKIPIF1<0，SKIPIF1<0，SKIPIF1<0，SKIPIF1<0時，都有SKIPIF1<0成立，則實數(shù)SKIPIF1<0的最小值為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<014．已知函數(shù)SKIPIF1<0，若SKIPIF1<0有四個不同的零點(diǎn)，則a的取值范圍為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D．SKIPIF1<015．已知函數(shù)SKIPIF1<0（SKIPIF1<0為自然對數(shù)的底數(shù)），關(guān)于SKIPIF1<0的方程SKIPIF1<0恰有四個不同的實數(shù)根，則SKIPIF1<0的取值范圍為（）A．SKIPIF1<0 B．SKIPIF1<0 C．SKIPIF1<0 D