﻿ Second, the power function and rational functions

### 二、幂函数与有理函数 Second, the power function and rational functions

[ 定义 ] 形如 [Definition] of the form 的函数称为幂函数，式中 a 为任意实常数 . Function called power function, wherein a is an arbitrary real constant.

x 的多项式 polynomial x

( a 0 , a 1 , L , a n 为常数， n 为自然数 ) (A 0, a 1, L, a n are constants, n is a natural number)

[ 幂函数的图形与特征 ] [Graphics and features a power function]

 方程与图形 Equations and graphics 特 征 Features 曲线通过点(0,0)和(1,1)；当 x >1 时 ， a 越大曲线上升越快. Curve through the point (0,0) and (1,1); when x> 1, a larger the curve rises faster. 当 a 为偶数，函数为偶函数，在区间 (0, ¥ ) 中为递增函数，在区间 (- ¥ ,0) 中为递减函数. When a is an even number, the function is an even function, in the interval (0, ¥) for increasing function in the interval (- ¥, 0) as a decreasing function. 当 a 为奇数，函数为奇函数和递增函数. When a is odd, odd function for function and increasing function. 曲线通过点 (1,1). Curve through the point (1,1). 当 a 为负偶数，函数为偶函数，在区间 (- ¥ ,0) 中为递增函数，在区间 (0, ¥ ) 中为递减函数. When a negative even, function even function in the interval (- ¥, 0) for increasing function in the interval (0, ¥) for decreasing function. 当 a 为负奇数，函数为奇函数和递减函数. When a negative odd function is an odd function and decreasing function.