高中函數(shù)基本知識點(diǎn)

高中函數(shù)學(xué)問點(diǎn).函數(shù)單調(diào)性(1)設(shè)則上是增函數(shù)；上是減函數(shù).(2)設(shè)函數(shù)在某個區(qū)間內(nèi)可導(dǎo)，假如，則為增函數(shù)；假如，則為減函數(shù).注：假如函數(shù)和都是減函數(shù),則在公共定義域內(nèi),和函數(shù)也是減函數(shù);假如函數(shù)和在其對應(yīng)定義域上都是減函數(shù),則復(fù)合函數(shù)是增函數(shù).奇偶函數(shù)圖象特征奇函數(shù)圖象關(guān)于原點(diǎn)對稱，偶函數(shù)圖象關(guān)于y軸對稱;反過來，假如一個函數(shù)圖象關(guān)于原點(diǎn)對稱，則這個函數(shù)是奇函數(shù)；假如一個函數(shù)圖象關(guān)于y軸對稱，則這個函數(shù)是偶函數(shù)．注：假設(shè)函數(shù)是偶函數(shù)，則；假設(shè)函數(shù)是偶函數(shù)，則.注：對于函數(shù)(),恒成立,則函數(shù)對稱軸是函數(shù);兩個函數(shù)與圖象關(guān)于直線對稱.注：假設(shè),則函數(shù)圖象關(guān)于點(diǎn)對稱;假設(shè),則函數(shù)為周期為周期函數(shù).多項(xiàng)式函數(shù)奇偶性多項(xiàng)式函數(shù)是奇函數(shù)偶次項(xiàng)(即奇數(shù)項(xiàng))系數(shù)全為零.多項(xiàng)式函數(shù)是偶函數(shù)奇次項(xiàng)(即偶數(shù)項(xiàng))系數(shù)全為零.23.函數(shù)圖象對稱性(1)函數(shù)圖象關(guān)于直線對稱.(2)函數(shù)圖象關(guān)于直線對稱.兩個函數(shù)圖象對稱性(1)函數(shù)與函數(shù)圖象關(guān)于直線(即軸)對稱.(2)函數(shù)與函數(shù)圖象關(guān)于直線對稱.(3)函數(shù)和圖象關(guān)于直線y=x對稱.圖象右移、上移個單位，得到函數(shù)圖象；假設(shè)將曲線圖象右移、上移個單位，得到曲線圖象.互為反函數(shù)兩個函數(shù)關(guān)系.存在反函數(shù),則其反函數(shù)為,并不是,而函數(shù)是反函數(shù).幾個常見函數(shù)方程(1)正比例函數(shù),.(2)指數(shù)函數(shù),.(3)對數(shù)函數(shù),.(4)冪函數(shù),.(5)余弦函數(shù),正弦函數(shù)，，.幾個函數(shù)方程周期(約定a>0)〔1〕，則周期T=a；〔2〕，或，或,或,則周期T=2a；(3)，則周期T=3a；(4)且，則周期T=4a；(5),則周期T=5a；(6)，則周期T=6a.分?jǐn)?shù)指數(shù)冪(1)〔，且〕.(2)〔，且〕.根式性質(zhì)〔1〕.〔2〕當(dāng)為奇數(shù)時，；當(dāng)為偶數(shù)時，.有理指數(shù)冪運(yùn)算性質(zhì)(1).(2).(3).注：假設(shè)a＞0，p是一個無理數(shù)，則ap表示一個確定實(shí)數(shù)．上述有理指數(shù)冪運(yùn)算性質(zhì)，對于無理數(shù)指數(shù)冪都適用..34.對數(shù)換底公式(,且,,且,).推論(,且,,且,,).對數(shù)四則運(yùn)算法則假設(shè)a＞0，a≠1，M＞0，N＞0，則(1);(2);(3).注：設(shè)函數(shù),記.假設(shè)定義域?yàn)?則，且;假設(shè)值域?yàn)?則，且.對于情形,須要單獨(dú)檢驗(yàn).對數(shù)換底不等式及其推論假設(shè),