我就是教這種國際課程的老師,看看我的解釋是否能令你滿意.
end behavior 大致可以理解為 "終（/末）端 走（/趨）勢" .也就是描述當x趨向于正負無窮的時候多項式(polynomial)所趨向的值.sketch 的意思是 “畫草圖”.所以這道題其實是要求 描述該多項式在x趨于正負無窮時的極值并畫出草圖.
舉個例子說：
Describe the end behavior of f (x) = 2x^4 - 6x^2+x +
as x→ +∞,f(x)→ +∞ and as x→ -∞,f(x)→ +∞ too.
總的來說：Every polynomial whose degree is greater than or equal to 1 becomes infinite as x dose.
下面我給出你一種英文的解釋（描述的更詳細一些）:
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.