高中階段12種常見函數(shù)的圖像及其性質(zhì).doc

1、函數(shù)名一次函數(shù)二次函數(shù)反比例函數(shù)指數(shù)函數(shù)解析式/(x)二處+如工0)f (x) = axA +bx + c(心0)XfM = ax(Q0 且 QH1)圖像a0 j/ /1OX-a0JYkQy jox叮抵yr = aX(Osvlh 卜也/ (a 1)AOlxrXZL 一x.定義域RR1xxAR值域RAac-b2、嚴(yán))4a(? 8 ,0)50,+ 00)(0,4-co)必過點(diǎn)(0上)(0, c)(k,l)(乂-1)(0,1)周期性不是周期函數(shù)不是周期函數(shù)不是周期函數(shù)不是周期函數(shù)單調(diào)性在R上單增(? OO,3)為減 2a(一,+ 0 )為增2a(-00,0)為減(0, + OO)為減d 1為增，0a

2、 Olla工1)Y=xay = 4x 如U0)y cix H ci j） X中學(xué)研究方便通常只了解方0的情況y =了研卜|+卜_/?為 :究方便設(shè)a b圖像y I y = Ax 1( 3)y=.v2.方JJ/y2觀; Vb-a0L / II-a b X10 z(0 a 1,單調(diào)遞增。0 v a v 1,單調(diào)遞 減。定義域內(nèi)為增函數(shù)-oo,遞增，遞減閉遞減，耳日勺遞增。（-00, aAJ減函數(shù) 卜,+oc）為增函數(shù)。 d,切上為常值函 數(shù)。MS無最人最小值?min =；無最人值無最人最小值)?min =ba奇偶性非奇非偶非奇非偶奇函數(shù)a + h = O為偶函數(shù)對(duì)稱性既不是軸對(duì)稱也不是H4心對(duì)稱既

3、不是軸對(duì)稱也不是中心對(duì)稱關(guān)于原點(diǎn)成中心對(duì)稱關(guān)于直線a + bX 劉稱O2漸近線直線x=0y = axAx = O函數(shù)名正弦函數(shù)余弦函數(shù)正切函數(shù)正弦型函數(shù)解析式y(tǒng) = sin xy- cos xy = tan xxAk7T + ,k G z2y = Asin(69x + (p) (40g0)圖像y3/ry i! y| 1：1 11JJ;/0-X0兀1?兀2o -iAy 兀lx11定義域RR 71XIXHRTT,k G ZR值域-U-hlR-A 人必過點(diǎn)(煙,0)rr(kzr,0)2(so)周期性5712龍CO單調(diào)性2A-,2A + -.2 2_為增函數(shù)兒兒2k7l H2k 兀 H 2 2為減函數(shù)lk7i + 兀 2k 兀 + 2 打 為增函數(shù)2k7T,2k7T + 7r為減函數(shù)1 22 J為增函數(shù)求解最值max =1八min = - 13?max = 1 兒 lin = i無最大最小值Vmax = A, ) ?min = _ 人奇偶性奇函數(shù)偶函數(shù)奇函數(shù)不確定對(duì)稱性即是中心對(duì)稱乂是軸對(duì)稱。對(duì)稱中心為編嚼為直線71x x = k7l + .k ? z即是軸對(duì)稱又是中心對(duì)稱。對(duì)稱中心為TT(k7T H ,0)對(duì)稱車磯直線xx