# How do you graph y=sqrtx-3, compare it to the parent graph and what is the domain and range?

Aug 27, 2017

Standard graph of $y = \sqrt{x}$ transformed (shifted) 3 units negative (down) on the $y -$axis.
Domain; [0, +oo); Range: [-3, +oo)

#### Explanation:

$y = \sqrt{x} - 3$

Graphically, $y$ is the standard graph of $y = \sqrt{x}$ transformed (shifted) 3 units negative (down) on the $y -$axis. As can be seen by the graph of $y$ beow.

graph{sqrtx-3 [-1.28, 16.5, -4.204, 4.686]}

$y \in \mathbb{R}$ is defined where $x \ge 0$

Hence, the domain of $y$ is $\left[0 , + \infty\right)$

Then, ${y}_{\min} = y \left(0\right) = - 3$

Since $y$ has no upper bound, the range of $y$ is [-3, +oo)