Explanation
[tex]\begin{gathered} g(x)=(x+4)^2-3 \\ \end{gathered}[/tex]
The domain of a function is the complete set of possible values of the independent variable.so , we the domain is restricted to
[tex]\begin{gathered} (-\infty,-4) \\ \end{gathered}[/tex]
it means,x can take only values smaller than -4,so the graph goes from -4 ( not included) to the left
I hope this helps you
