本文就函数f(x)=x+k/x(k0)的图像,性质及其变形和应用进行归纳总结并展开讨论.结论1函数f(x)=x+k/x(k0)的图象及性质:(1)图象如右图所示:(2)性质:①是奇函数;②在区间(k,+∞)和(?∞,?k)上单调递增,在区间(?k,0),和(0,k)上单调递减;③在x0时,有最小值2k,在x0时,有最大值?2k; This paper summarizes and discusses the image of f(x)=x+k/x(k0), its properties and its deformation and application. Conclusion 1 Graph of function f(x)=x+k/x(k0) Image and nature: (1) The image is shown on the right: (2) Properties: 1 is an odd function; 2 monotonically increasing in the interval (k, +∞) and (?∞, ?k) in the interval (? k, 0), and (0, k) monotonically decreasing; 3 in x0, there is a minimum of 2k, in x0, there is a maximum of ? 2k;