Glencoe Algebra 2, Chapter 2, 2.6, Section 2.6, Problem 32

g(x) = |x| +3 , the the domain and range is given as follows
(i)Domain definition:
The domain of a function is the set of the input or argument values for which the function is real and defined.
In this function, the function has no undefined points, so the domain is
-oo (ii)Range definition
It is the set of values of the dependent variable for which a function is defined.
For this function the interval has a minimum point at x= 0 with value g(x) = 3
so the range of |x|+3 is g(x) >= 3 or, [3,oo)
It can also be observed from the graph below: