Answer:
[tex]-\sqrt{x + 4}[/tex]
Step-by-step explanation:
1- It's known that shifting(called translation), reflection and rotation operations on th function would let us manipulate it as we like, and taking the square root function
[tex]\sqrt{x}[/tex]
would let us to start graphing from the desired point in the xy-plane by using shifting operations on it.
2- Taking the minus of the square root function
[tex]-\sqrt{x}[/tex]
would reflect the function over x-axis so the function would be decreasing from 0 to infinity.
3- Then, adding 4 to x in the square root
[tex]-\sqrt{x+4}[/tex]
would make the domain of the function to start from [tex] x+4 > 0[/tex]or [tex]x > - 4[/tex] (by adding 4 to both sides).
4- Finally, the function of the domain (-4, [tex]\infty[/tex]) is
[tex]-\sqrt{x+4}[/tex].
I hope that I helped, and i'm sorry for any English mistakes(I'm not English speaker) .
