1、Vertical asymptote,Wang zhiqiang 王志強(qiáng),2012-11-7,The High School Attached to Northwest Normal University,1、Observe the following two functions,Are there the same two functions?,2, 、Review,We observe that is not continuous at x=2. That is to say, at x=2 , f(x) is not defined. But If we redefine f(2)=4,

2、 the new function will be continuous everywhere. This discontinuity is called removable discontinuity (可取間斷點(diǎn)).,上面的例題中，圖像上會(huì)出現(xiàn)一個(gè)洞（hole）,而出現(xiàn)洞的原因是函數(shù)分母不能為零，因此要挖去 x=2 對(duì)應(yīng)的點(diǎn)，但是所有使得分母為0的點(diǎn)都會(huì)在圖像上對(duì)應(yīng)一個(gè)洞嗎？,2、Observe the following function,: f(x)=x/x-1.gsp,可見并非所有使得分母為0的點(diǎn)都會(huì)在圖像上對(duì)應(yīng)一個(gè)洞，只有使分子與分母同時(shí)為0時(shí)，在圖像上才會(huì)對(duì)應(yīng)一個(gè)洞。,Examp

3、le 1:,當(dāng)x=-2時(shí)，f(x) 的圖像上對(duì)應(yīng)一個(gè)洞；,當(dāng)x=2 時(shí)，f(x) 的圖像上不會(huì)形成洞。,: figure9,現(xiàn)在我們來(lái)研究當(dāng)分母為零，而分子不為0時(shí)，f(x)在x=x0處有什么特征？,而如果要把這個(gè)洞補(bǔ)上，即重新定義f(-2)的值，則可使該函數(shù)變?yōu)檫B續(xù)函數(shù)。,、vertical asymptote,: f(x)=x/x-1,: figure9,We can find:,因此，我們得到了一個(gè)找有理函數(shù)的豎直漸近線的方法：,且x=1為f(x)的一條豎直漸近線（Vertical asymptote）,1）,2）,且x=2為f(x)的一條豎直漸近線（Vertical asymptote）,Let ,if , then is a vertical asymptote of .,Remarks:,The line x=a is a vertical asymptote of the graph y=f(x) if one or more of the following holds:,Example 4: Find asymptote of,: figure10, 、Class Sum