Moving function with vector (absolute values)

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I have problem with functions and moving them with a vector. My first function is on image below f(x) function

Now I must draw graph of another function g(x)=f(|x|+2) That's right. First, I must move function left 2 points then "delete" everything on left side of value axis (y) then reflect everything on left side.

But I have problem with next two functions:
1 g(x) = f(-|x|+2) Is that right? I think that I need to do the same as in the case of the first function but reflect everything on RIGHT side. Am I right?

2 g(x) = f(|x+2|) This is last function. I don't know what I must do with it. Will it look different than function g(x)=f(|x|+2)? I don't know. Please help me. I will be very graceful if You present your answer using the picture (function graph) :-)