We have the function f(x)=2|x+1|
The graph is:
The domain is "all the real numbers", as there is no singularity in the function that makes it be undefined. So f(x) is defined for any value of x.
The range is "all the real numbers equal or bigger than 0", as the function is always positive: it is a positive number multiplying an absolute value that is always positive (or zero).