# How do you graph y=sqrtx-1, compare it to the parent graph and what is the domain and range?

Jan 7, 2018

domain: $x \ge 0$
range: $y \ge - 1$
same shape as parent function, just shifted down 1 unit.

#### Explanation:

Start with the parent function: $y = \sqrt{x}$, which has domain $x \ge 0$ and range $y \ge 0$.

Our new graph is of $y = \sqrt{x} - 1$. The $- 1$ represents a vertical shift of 1 unit down. It is a "rigid transformation" in that the shape of the graph remains exactly the same, you just pick up the whole thing and move it down 1 unit.

Since there is no shift left or right, the domain of $y = \sqrt{x} - 1$ is the same as the domain of $y = \sqrt{x}$, so $x \ge 0$. Since everything was shifted down 1 unit, the range changes from the range of the original, $y \ge 0$, to $y \ge - 1$, shifting it down 1 unit.