蘇教版必修一指數(shù)函數(shù)對數(shù)函數(shù)和冪函數(shù) 冪函數(shù)

冪函數(shù)(2)1.冪函數(shù)的定義:形如的函數(shù)叫做冪函數(shù).

其中x是自變量,是常數(shù).知識回顧定義域Oxy11-1-1Oxy11-1-1Oxy11-1-1Oxy11-1-1Oxy11-1-1Oxy11-1-1RRR[0，+∞）(-∞,0)∪(0,+∞)(-∞,0)∪(0,+∞)奇函數(shù)偶函數(shù)奇函數(shù)奇函數(shù)偶函數(shù)非奇非偶(-∞,+∞)增(-∞,0)減(0,+∞)增(-∞,+∞)增[0,+∞)增1、過(0，0)點、(1，1)點。2、在[0,+∞)上是單調(diào)增函數(shù)。1、過(1，1)點2、在(0,+∞)上是減函數(shù)。共性單調(diào)性奇偶性名稱圖象(-∞,0)減

(0,+∞)

減(-∞,0)增

(0,+∞)

減2.冪函數(shù)的性質(zhì):(2).在第一象限,冪指數(shù)大于0的冪函數(shù)圖象___,在(0,+∞)是____函數(shù)(3).在第一象限,冪指數(shù)小于0的冪函數(shù)圖象____,在(0,+∞)是___函數(shù)(1).冪函數(shù)的圖象都過點_____(1,1)增上升下降減復(fù)習練習1.求函數(shù)的定義域.2.比較大小:復(fù)習練習兩個冪的大小比較:(1).同底數(shù)的冪借助于指數(shù)函數(shù)的單調(diào)性;(2).同指數(shù)的冪借助于冪函數(shù)的單調(diào)性或作商比較;(3).既不同底數(shù)也不同指數(shù)的冪借助于中間值比較;1.已知函數(shù),(1)若函數(shù)f(x)是冪函數(shù),則m=___________(2)若函數(shù)f(x)是冪函數(shù),且f(x)在區(qū)間(0,+∞)上是減函數(shù),則m=___________(3)若函數(shù)f(x)是正比例函數(shù),則m=_________(4)若函數(shù)f(x)是反比例函數(shù),則m=_________例題精講2.已知冪函數(shù)（m∈Z）為偶函數(shù)，且在區(qū)間（0，+∞）上是單調(diào)遞減函數(shù).求函數(shù)f（x）的解析式；例題精講例題精講3.判定下列各式中參數(shù)的取值范圍.4.已知點在冪函數(shù)f(x)的圖象上,點在冪函數(shù)g(x)的圖象上,問x為何值時,f(x)>g(x)?Oxyx1x2變式:x為何值時,f(x)<g(x)?例題精講1.不等式的解集是___________2.不等式的解集是___________3.已知函數(shù)在上是增函數(shù),在上是減函數(shù),則最小的正整數(shù)a=_______4.已知冪函數(shù)的圖象不過原點,則實數(shù)m的值是_________.鞏固練習5.如圖所示的曲線是冪函數(shù)y=xn的圖象.已知n取四