Given function: `g(x) = log_4(x-3)`
The domain of a function is defined as all the values of x for which the function exists or is defined. Recall that logarithmic functions are not defined for zero or negative numbers,
i.e., x-3> 0
or, x >3
therefore, the domain of the given function is (3,+`oo`]
The range of a function is defined as all the values of g(x) (in this case) for which some x exists such that the function will be defined.
The range of a logarithmic function is the set of real numbers or, g(x) `inRR`
You can use spreadsheet software for plotting the graph. I used Desmos calculator (https://www.desmos.com/calculator) and obtained the graph. Feel free to use any other utility as well.
Hope this helps.