题目

what is the end behavior of this polynomial function,sketch it roughly. 高等数学问题.求助准确翻译

提问时间：2021-02-25

答案

我就是教这种国际课程的老师,看看我的解释是否能令你满意.
end behavior 大致可以理解为 "终（/末）端 走（/趋）势" .也就是描述当x趋向于正负无穷的时候多项式(polynomial)所趋向的值.sketch 的意思是 “画草图”.所以这道题其实是要求 描述该多项式在x趋于正负无穷时的极值并画出草图.
举个例子说：
Describe the end behavior of f (x) = 2x^4 - 6x^2+x +
as x→ +∞,f(x)→ +∞ and as x→ -∞,f(x)→ +∞ too.
总的来说：Every polynomial whose degree is greater than or equal to 1 becomes infinite as x dose.
下面我给出你一种英文的解释（描述的更详细一些）:
The appearance of a graph as it is followed farther and farther in either direction.For polynomials,the end behavior is indicated by drawing the positions of the arms of the graph,which may be pointed up or down.Other graphs may also have end behavior indicated in terms of the arms,or in terms of asymptotes or limits.
Polynomial End Behavior:
1.If the degree n of a polynomial is even,then the arms of the graph are either both up or both down.
2.If the degree n is odd,then one arm of the graph is up and one is down.
3.If the leading coefficient an is positive,the right arm of the graph is up.
4.If the leading coefficient an is negative,the right arm of the graph is down.