函數(shù)y=eq\f(43,(x2-24)\r(x2+15))的圖像示意圖主要內(nèi)容：介紹函數(shù)y=eq\f(43,(x2-24)\r(x2+15))的定義域、值域、單調(diào)性及極限等性質(zhì)，同時簡要畫出函數(shù)的圖像示意圖?！?函數(shù)的定義域∵x2+15≥15＞0，x2-24≠0，則x≠±2eq\r(6),∴函數(shù)的定義域為：（-∞,-2eq\r(6))∪(2eq\r(6)，+∞)?！?函數(shù)的單調(diào)性∵y=43*[(x2-24)eq\r(x2+15)]?1∴eq\f(dy,dx)=-43*[(x2-24)eq\r(x2+15)]?2*[2xeq\r(x2+15)+eq\f(x(x2-24),eq\r(x2+15))]=-43*x[(x2-24)eq\r(x2+15)]?2*eq\f(2(x2+15)+(x2-24),eq\r(x2+15))=-43*x[(x2-24)eq\r(x2+15)]?2*eq\f(3x2+6,eq\r(x2+15));∵3x2+6>0,∴函數(shù)的單調(diào)性為：(1).當x∈(2eq\r(6),+∞)時，eq\f(dy,dx)<0，函數(shù)y在定義域上為減函數(shù)；(2).當x∈(-∞,2eq\r(6))時，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(43,(x2-24)\r(x2+15))∴f(-x)=eq\f(43,[(-x)2-24]\r([(-x)2+15]))=eq\f(43,(x2-24)\r(x2+15))=f(x),即函數(shù)為偶函數(shù)，在定義域上關(guān)于y軸對稱。※.函數(shù)的極限lim（x→-∞）eq\f(43,(x2-24)\r(x2+15))=0lim（x→+∞）eq\f(43,(x2-24)\r(x2+15))=0lim（x→-2eq\r(6)）eq\f(43,(x2-24)\r(x2+15))=+∞lim（x→2eq\r(6)）eq\f(43,(x2-24)\r(x2+15))=+∞※.函數(shù)的部分點圖表x-9.80-9.31-8.82-8.33-7.84-7.35-5.88x2-2472.0462.6853.7945.3937.4730.0210.57eq\r(x2+15)10.5410.089.639.198.748.317.04y0.0570.0680.0830.1030.1310.1720.578x5.887.357.848.338.829.319.80x2-2410.5730.0237.4745.3953.7962.6872.04eq\r(x2+15)7.048.318.749.199.6310.0810.54y0.5780.1720.1310.1030.0830.0680.057※.函數(shù)的圖像示意圖yy=eq\f(43,(x2-24)\r(x2+15))(-5.88,0.578)(-5.88,0.578)(-7.35,0.172)(-7.35,0.172)(-