Okay, here we have this:
We need to determinate if the function is even, odd, or neither, let's do it:
Considering that a function is even if f(-x)=f(x) for all the real numbers, and that a function is odd if f(-x)=-f(x) for all the real numbers.
Let's find first f(-x) and -f(x):
f(-x)=|-x+2|
-f(x)=-|x+2|
Now let's check if it is even:
f(x)=|x+2|, f(-x)=|-x+2|
Here we can see that f(-x) is diferent of f(x), so the function is not even.
Now let's check if it is odd:
-f(x)=-|x+2|, f(-x)=|-x+2|
Here we can see that -f(x) is diferent of f(-x), so the function is nor odd.
Finally we obtain that the correct answer is neither, it is neither even nor odd.