#y=sqrtx-2# is graphed by shifting the graph of #y=sqrtx# down two. #y=sqrtx# is basically half of a sideways parabola opening to the right for positive y-values. #y=sqrtx# implies #y=+sqrtx#, where y equals the positive square root of x, so inputting a value such as 9 for x yields 3 (as opposed to #y=+-sqrtx# which, for 9, yields 3 and -3). Additionally, x cannot be a negative value, so the graph for #y=sqrtx# starts at the origin (#y=sqrt(0)=0#) and curves up and to the right in the first quadrant. #y=sqrtx-2# is a transformation of #y=sqrtx# two units down (as #y=x-2# is a transformation of #y=x# two units down). Thus, the graph of #y=sqrtx-2# is:

graph{x^(1/2)-2 [-10, 10, -5, 5]}