有理函数的问题求大神帮忙分析讲解！明天考试！

有理函数的问题求大神帮忙分析讲解！明天考试！

a) Find a possible formula for a rational function f with these properties

(i) f has x-intercepts at 0, -2, and -4.

(ii) x = −1 is an asymptote for f

(iii) f is decreasing on ( 2− ,−1), and increasing on ( 1− ,0)

(iv) as x f → ∞ , (x)→2

(v) f x( ) ≥ 0 for x < −2

答案给出：f(x)=2x(x+2)(x+4)^2 / (x+1)^4

求帮忙分析一下如何得出的这个式子，下面分母的四次方怎么来的？

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From (i), f(x) has factors x, x+2 and x+4

From (ii), f(x) has x+1 in denominator

From (iii), f(x) has a minimum at x=-1, so the power of x+1 is even

From (iv), f(x) has a limit, so degrees...

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