例1数列{x n}满足x1=0,x n+1=-x2n+x n+c(n∈N+),(Ⅰ)证明:{x n}是递减数列的充分必要条件是c<0.(Ⅱ)求c的取值范围使{x n}是递增数列.本题是2012年全国高考安徽卷理科第21题,就第2问笔者利用数形结合思想给出它的另一解法.首先,为了下面表述的需要本文给出数列{a n}特征函数及其相关概念:对于数列{a n},若a n+1=f(a n),则称函数y=f(x)为数列{a n}的特征函数,称函数f(x)的图象与直线y=x的交点为函 Example 1 The sequence {xn} satisfies x1 = 0, x n + 1 = -x2n + x n + c (n∈N +), (Ⅰ) Prove that if xn is a decreasing sequence if c <0. Ⅱ) Find the value range of c so that {xn} is an increasing number of columns. This is the 2012 national college entrance examination in Anhui Volume 21, on the second asked the author to use the idea of ​​combination of figures to give it another solution. First of all, Here we show the {an} eigenvalues ​​and their related concepts: For an {a}, let y = f (x) be the sequence {an} if a n + 1 = f The eigenfunction, the intersection of the image of the function f (x) and the line y = x is a letter