1、主講人：薛等紅,歡迎各位老師蒞臨指導(dǎo)！,歡迎各位老師蒞臨指導(dǎo)！,鄂爾多斯市第三中學(xué),一、教材分析,二、教學(xué)重點(diǎn)、難點(diǎn),三、教學(xué)目標(biāo),四、教學(xué)方法,五、教學(xué)過(guò)程,六、教材設(shè)計(jì)說(shuō)明,作函數(shù)的圖象的常用方法,1. 描點(diǎn)作圖法;,2. 變換作圖法.,函數(shù)圖象變換,函數(shù)圖像的平移變換規(guī)律：,向上平移個(gè)單位,向下平移個(gè)單位,左右平移左加右減,上下平移上加下減,本質(zhì)上是函數(shù)圖像上的每個(gè)點(diǎn)的平移,一、新課引入,2、如何由函數(shù)的圖像作出函數(shù)的圖像？,問(wèn)題思考：,1、如何由函數(shù)的圖像得到函數(shù)的圖像？,向右平移個(gè)單位,向左平移個(gè)單位, 0 且 0,圖象向左平移 a 個(gè)單位,圖象向右平移 a 個(gè)單位,圖象向上平移 b

2、 個(gè)單位,圖象向下平移 b 個(gè)單位,a 0 且 b 0,二、問(wèn)題探究,在同一坐標(biāo)系下作出函數(shù)與，的圖像，觀察函數(shù)圖像的特征，你能得出什么結(jié)論？,x,y,y,y,x,關(guān)于y軸對(duì)稱,關(guān)于x軸對(duì)稱,關(guān)于原點(diǎn)對(duì)稱,函數(shù)圖像的對(duì)稱變換規(guī)律：,1、,3、,2、,關(guān)于y軸對(duì)稱,關(guān)于x軸對(duì)稱,關(guān)于原點(diǎn)對(duì)稱,0,-2,-3,-1,1,2,3,4,1,2,-1,-2,x,0,-2,-1,1,2,3,4,1,2,-1,-2,-3,0,-2,-1,1,2,3,4,1,2,-1,-2,-3,（x,y)換成（-x,y),（x,y)換成（-x,-y),（x,y)換成（x,-y),三、適應(yīng)練習(xí),3、如何由函數(shù)的圖像得到函數(shù)的

3、圖像？,向左移1個(gè)單位,關(guān)于y軸對(duì)稱,x,y,0,-2,-1,1,2,3,4,1,2,-1,-2,-3,-3,-4,3,4,x,y,0,-2,-1,1,2,3,4,1,2,-1,-2,-3,-3,-4,3,4,向右移1個(gè)單位,關(guān)于y軸對(duì)稱,或：,1、與的圖像關(guān)于_對(duì)稱；,2、與的圖像關(guān)于_對(duì)稱；,x 軸,y 軸,解：,注意：當(dāng)自變量的系數(shù)為負(fù)時(shí)，注意平移變換的方向,四、問(wèn)題探究,畫(huà)出函數(shù)的圖像，并指出它與的圖像有何聯(lián)系？,函數(shù)圖像的翻折變換規(guī)律：,由,保留y軸右側(cè)圖像，再將y軸右方圖像對(duì)稱翻折到y(tǒng)軸左方,保留x軸上方圖像，再將x軸下方圖像對(duì)稱翻折到x軸上方,由,x,y,0,-2,-1,1,2,

4、3,4,1,2,-1,-2,-3,-3,-4,3,4,x,y,0,-2,-1,1,2,3,4,1,2,-1,-2,-3,-3,-4,3,4,注意區(qū)分 與 的表現(xiàn)形式哦!,五、適應(yīng)練習(xí),分別作出下列函數(shù)的圖像：,1、,2、,x,y,0,-2,-1,2,3,4,2,-1,-2,-3,-3,-4,4,x,y,0,-2,-1,1,2,3,4,1,2,-1,-2,-3,-3,-4,3,4,3,1,1,解：,保留y軸右側(cè)圖像，再將y軸右方圖像對(duì)稱翻折到y(tǒng)軸左方,保留x軸上方圖像，再將x軸下方圖像對(duì)稱翻折到x軸上方,圖1,圖2,1、,2、,六、實(shí)例講解,例1、作出下列函數(shù)的圖像，并指出函數(shù)的定義域、值域、奇

5、偶性、單調(diào)性：,x,y,0,-2,-1,1,2,3,4,1,2,-1,-2,-3,-3,-4,3,4,1、,2、,x,y,0,-2,-1,1,2,3,4,1,2,-1,-2,-3,-3,-4,3,4,解：1、,2、,保留y軸右側(cè)圖像，再將y軸右方圖像對(duì)稱翻折到y(tǒng)軸左方,向下移1個(gè)單位,保留x軸上方圖像，再將x軸,下方圖像對(duì)稱翻折到x軸上方,六、實(shí)例講解,例2：求關(guān)于x的方程的不同實(shí)根的個(gè)數(shù)。,0,y,x,-4,1,4,-1,y=a(a=0) 有兩個(gè)交點(diǎn),y=a(0a4) 有四個(gè)交點(diǎn),y=a(a=4) 有三個(gè)交點(diǎn),y=a(a4) 有二個(gè)交點(diǎn),解：在同一坐標(biāo)系中，作出y=|x2+2x-3|和y=a

6、的圖像。,當(dāng)a0時(shí),當(dāng)a=0時(shí),當(dāng)0a4時(shí),當(dāng)a=4時(shí)，,當(dāng)a4時(shí),方程無(wú)解;,方程有兩個(gè)解;,方程有四個(gè)解;,方程有三個(gè)解;,方程有兩個(gè)解.,y=a(a0) 沒(méi)有交點(diǎn),當(dāng)a4或a=0時(shí),方程有兩個(gè)解.,-2,2,1,2,3,-1,-2,-3,-3,3,由圖可知：,關(guān)于直線yx對(duì)稱,七、抽像概括,1、圖像變換法： （1）對(duì)稱變換法 （2）翻折變換法,2、用圖像變換法畫(huà)函數(shù)圖像時(shí)，往往要找出該函數(shù)的基本初等函數(shù)，分析其通過(guò)怎樣變換得到所求函數(shù)圖像，有時(shí)要先對(duì)解析式進(jìn)行適當(dāng)變形。,3、利用函數(shù)的圖像判定單調(diào)性、求方程根的個(gè)數(shù)、解不等式、求最值等，體現(xiàn)了數(shù)形結(jié)合的數(shù)學(xué)思想。,關(guān)于y軸對(duì)稱,關(guān)于x軸對(duì)稱,關(guān)于原點(diǎn)對(duì)稱,保留x軸上方圖