Question 127814
Your problem statement is ambiguous:


Is it {{{y=(1/2)sqrt(x) + 3}}}, or


{{{y=(1/2)(sqrt(x) + 3)}}}, or


{{{y=(1/2)sqrt(x + 3)}}}? 



As to the domain, in the first two functions, [{{{0}}},{{{infinity}}}), and for the third function, [{{{-3}}},{{{infinity}}})


As to the range:

First function:  [{{{3}}},{{{infinity}}})


Second function: [{{{3/2}}},{{{infinity}}})


Third function:  [{{{0}}},{{{infinity}}})


Red is the first way, green is the second way, and blue is the last way:


{{{drawing(600,600,-5,5,-1,4,grid(1),
graph(600,600,-5,5,-1,4,(1/2)sqrt(x) + 3,(1/2)(sqrt(x) + 3),(1/2)sqrt(x + 3))
)}}}