[考綱傳真] 1.理解有理指數(shù)冪的含義,了解實(shí)數(shù)指數(shù)冪的意義,掌握冪的運(yùn)算.2.了解指數(shù)函數(shù)模型的實(shí)際背景.3.理解指數(shù)函數(shù)的概念及其單調(diào)性,掌握指數(shù)函數(shù)圖像通過的特殊點(diǎn),會(huì)畫底數(shù)為2,3,10,,的指數(shù)函數(shù)的圖像.4.體會(huì)指數(shù)函數(shù)是一類重要的函數(shù)模型.
1.有理指數(shù)冪
(1)分?jǐn)?shù)指數(shù)冪
①正分?jǐn)?shù)指數(shù)冪:a=(a>0,m,n∈N*,且n>1);
②負(fù)分?jǐn)?shù)指數(shù)冪:a==(a>0,m,n∈N*,且n>1);
③0的正分?jǐn)?shù)指數(shù)冪等于0,0的負(fù)分?jǐn)?shù)指數(shù)冪沒有意義.
(2)有理數(shù)指數(shù)冪的運(yùn)算性質(zhì)
①ar·as=ar+s(a>0,r,s∈Q);
②(ar)s=ars(a>0,r,s∈Q);
③(ab)r=arbr(a>0,b>0,r∈Q).
2.指數(shù)函數(shù)的圖像與性質(zhì)