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            2017年成人高考高起點數學復習資料-難點講解(四)

            福建成人高考信息網www.laiwobuy.com 發布時間: 2017年04月08日

            難點四:三個“二次”及關系

              三個“二次”即一元二次函數、一元二次方程、一元二次不等式是中學數學的重要內容,具有豐富的內涵和密切的聯系,同時也是研究包含二次曲線在內的許多內容的工具。高考試題中近一半的試題與這三個“二次”問題有關。本節主要是幫助考生理解三者之間的區別及聯系,掌握函數、方程及不等式的思想和方法。

              4、難點磁場

              已知對于x的所有實數值,二次函數f(x)=x2-4ax+2a+12(a∈R)的值都是非負的,求關于x的方程 =|a-1|+2的根的取值范圍。

              

            難點五:求解函數解析式

              求解函數解析式是高考重點考查內容之一,需引起重視。本節主要幫助考生在深刻理解函數定義的基礎上,掌握求函數解析式的幾種方法,并形成能力,并培養考生的創新能力和解決實際問題的能力。

              5、難點磁場

              已知f(2-cosx)=cos2x+cosx,求f(x-1)。

              案例探究

              [例1](1)已知函數f(x)滿足f(logax)= (其中a>0,a≠1,x>0),求f(x)的表達式。

              (2)已知二次函數f(x)=ax2+bx+c滿足|f(1)|=|f(-1)|=|f(0)|=1,求f(x)的表達式。

              

            難點六:函數值域及求法

              函數的值域及其求法是近幾年高考考查的重點內容之一。本節主要幫助考生靈活掌握求值域的各種方法,并會用函數的值域解決實際應用問題。

              6、難點磁場

              設m是實數,記M={m|m>1},f(x)=log3(x2-4mx+4m2+m)。

              (1)證明:當m∈M時,f(x)對所有實數都有意義;反之,若f(x)對所有實數x都有意義,則m∈M.

              (2)當m∈M時,求函數f(x)的最小值。

              (3)求證:對每個m∈M,函數f(x)的最小值都不小于1.


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