Question 835529
The function g(x) as given has the domain, all real numbers.  The critical point is at x=0.


For {{{x>=0}}}, {{{g(x)=x-3}}};
For {{{x<0}}}, {{{g(x)=-x-3}}}.
The y-intercept is (0,-3).
g(x) has a minimum, vertex point (0,-3).
This means RANGE is {{{g(x)>=-3}}}.


INTERVAL NOTATION:  
Domain, (-oo, +oo).
Range, [-3, +oo).


Shift upward 3 units and 4 units to the left:
{{{h(x)=abs(x+4)-3+3}}}, which is {{{h(x)=abs(x+4)}}}


The given, function g(x)
{{{graph(300,300,-10,10,-10,10,abs(x)-3)}}}


The changed function, h(x)
{{{graph(300,300,-10,10,-10,10,abs(x+4))}}}