Why does this function have a unique shape?

[abdo799]

basically, i am given a function and told to sketch it. f(x)=abs(x+4) + abs(3-x)
i didnt know how to do it, so i used this site ( http://rechneronline.de/function-graphs/ )
it gave this graph with a really weird shape , can anyone explain it??
i tried to google it to find the answer, but i didnt even know what to type and search

 

[LCKurtz]

Surely, if no other way, you could just make a table of values for x from say -6 to 6. How hard can that be? Try it.

 

[abdo799]

Surely, if no other way, you could just make a table of values for x from say -6 to 6. How hard can that be? Try it.

i did the sketch , i need to know why it has this shape

 

[LCKurtz]

i did the sketch , i need to know why it has this shape

Try writing your function as a muti-piece formula. For example, if $x < -4$ what would $|x+4|$ and $|3-x|$ be without the absolute value signs. Then try $-4<x<3$ and so on. Remember $|x| = x,~x>0$ and $|x| = -x,~x<0$.