Question 407741
f(x+2) corresponds to a horizontal shift of the y-axis 2 units to the right, and so the new domain is (-4, {{{infinity}}}). 
-f(x+2)-2 implies reflection across the x-axis,  and then vertical shift of x-axis 3 units up, and so the new range is [3 - 3, -4 - 3], or [0, -7].