Question

How do you graph `y=sqrtx-2` and compare it to the parent graph?

Answer 1

`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]}