Answer:
The graph of the function y = sqrt(x + 1) - 2 is a transformation of the graph of the parent function y = sqrt(x). The parent function y = sqrt(x) is the square root function in its simplest form, with no transformation applied to it.
The transformation y = sqrt(x + 1) - 2 affects the parent function in the following ways:
The function inside the square root sign (x + 1) is shifted one unit to the right, meaning that the graph is shifted one unit to the right.
The function is then shifted two units downward, meaning that the graph is shifted two units downward.
As a result, the graph of y = sqrt(x + 1) - 2 is the same as the graph of y = sqrt(x), but shifted one unit to the right and two units downward.
Both of the functions has the same vertex point which is (-1,-2) and the domain is x>=-1 and the range is y>=-2.
It also shares the same shape as the parent function, an upward opening parabola with vertex at the origin.
Explanation: