函數(shù)y=eq\f(96,(x2-34)\r(x2+71))的圖像示意圖主要內(nèi)容：介紹函數(shù)y=eq\f(96,(x2-34)\r(x2+71))的定義域、值域、單調(diào)性及極限等性質(zhì)，同時(shí)簡(jiǎn)要畫出函數(shù)的圖像示意圖?！?函數(shù)的定義域∵x2+71≥71＞0，x2-34≠0，則x≠±eq\r(34),∴函數(shù)的定義域?yàn)椋海?∞,-eq\r(34))∪(eq\r(34)，+∞)。※.函數(shù)的單調(diào)性∵y=96*[(x2-34)eq\r(x2+71)]?1∴eq\f(dy,dx)=-96*[(x2-34)eq\r(x2+71)]?2*[2xeq\r(x2+71)+eq\f(x(x2-34),eq\r(x2+71))]=-96*x[(x2-34)eq\r(x2+71)]?2*eq\f(2(x2+71)+(x2-34),eq\r(x2+71))=-96*x[(x2-34)eq\r(x2+71)]?2*eq\f(3x2+108,eq\r(x2+71));∵3x2+108>0,∴函數(shù)的單調(diào)性為：(1).當(dāng)x∈(eq\r(34),+∞)時(shí)，eq\f(dy,dx)<0，函數(shù)y在定義域上為減函數(shù)；(2).當(dāng)x∈(-∞,eq\r(34))時(shí)，eq\f(dy,dx)>0，函數(shù)y在定義域上為增函數(shù)?！?函數(shù)的奇偶性∵f(x)=eq\f(96,(x2-34)\r(x2+71))∴f(-x)=eq\f(96,[(-x)2-34]\r([(-x)2+71]))=eq\f(96,(x2-34)\r(x2+71))=f(x),即函數(shù)為偶函數(shù)，在定義域上關(guān)于y軸對(duì)稱?！?函數(shù)的極限lim（x→-∞）eq\f(96,(x2-34)\r(x2+71))=0lim（x→+∞）eq\f(96,(x2-34)\r(x2+71))=0lim（x→-eq\r(34)）eq\f(96,(x2-34)\r(x2+71))=+∞lim（x→eq\r(34)）eq\f(96,(x2-34)\r(x2+71))=+∞※.函數(shù)的部分點(diǎn)圖表x-11.66-11.08-10.50-9.91-9.33-8.75-7.00x2-34101.9688.7776.2564.2153.0542.5615.00eq\r(x2+71)14.3913.9213.4613.0112.5712.1510.95y0.0650.0780.0940.1150.1440.1860.584x7.008.759.339.9110.5011.0811.66x2-3415.0042.5653.0564.2176.2588.77101.96eq\r(x2+71)10.9512.1512.5713.0113.4613.9214.39y0.5840.1860.1440.1150.0940.0780.065※.函數(shù)的圖像示意圖yy=eq\f(96,(x2-34)\r(x2+71))(-7.00,0.584)(-7.00,0.584)(-8.75,0.186)