解一道英语的数学题,rational function!只用把三个式子列出来就好!Give an example of a rational function with (A) even symmetry (B) odd symmetry (C)neither even or odd symmetry.Include both the function’s equations and a nice graph

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解一道英语的数学题,rational function!只用把三个式子列出来就好!
Give an example of a rational function with (A) even symmetry (B) odd symmetry (C)
neither even or odd symmetry.Include both the function’s equations and a nice graph.For all of
your examples both the degree of the numerator and the degree of the denominator must be
more than two when the expression is fully reduced.

给出以下情形时的有理函数的例子各一,要求包括函数方程和一个漂亮的图：
（A）偶函数
（B）奇函数
（C）非奇非偶函数
所有给出的例子中分子和分母既约后的次数必须均高于2次
answer:
case A:f(x) = (x²+1) / (x^4 + 1)
case B:f(x) = x^3 / (x^4 + 1)
case C:f(x) = (x²+1) / (x^3 + 1)
画图用Matlab或GeoGebra之类的画一下就行了

rational function 有理函数一般是两个多项式的除法
（A）偶函数 x^4/(1+x^4)
（B）奇函数 x³/(1+x^4)
（C）非奇非偶函数 (1-x+x^3)/(1+x+x^4)

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