head down to和 lay down under中,down,to,under分别是什么词性?怎么辨别的?介词

head down to 朝着...去: down是副词,to是介词,因为副词后不可以接名词,所以后面再加介词后才能接名词.以下 四个词组都属于：动词+副词+介词 的结构例如：
They headed down to the foot of the mountain. 他们朝着山脚下进发.
At last they lay down under the tree and had a rest. 最后,他们在树下躺下来休息.
Don't look down upon people who are not as rich as you. 不要瞧不起那些不如你富有的人