You have the following parent function:
y = √x
after a transformation of 5 units right you obtain:
√x => √x + 5
a reflection around the x-axis results in:
√x + 5 => -√x - 5
a transformation of 2 units down is given by:
-√x - 5 => -√x - 5 - 2 = -√x - 7
and finally, a horizontal compression with factor 2, results in:
-√x - 7 => -√(2x) - 7
The graph of the previous result is shown below:
as you can notice, the domain and the range are:
domain: (0 , oo)
range: (-7 , -oo)
