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

Feb 4, 2018

Graph it using a graphing calculator, domain is $\left\{x | x \ge 0 , x \in R\right\}$, range is $\left\{y | y \le - 3 , y \in R\right\}$

#### Explanation:

If you do not have a graphing calculator, you can use one that is online and free, such as Desmos. Here is the link: Desmos

There are buttons at the bottom of the screen that can be used to enter your function. The parent function is $\sqrt{x}$. You can also graph that function to see how it compares to your transformed function.

The way to write your function in standard form is as following:
$a \cdot \sqrt{b \left(x + c\right)} + d$, where b and c are horizontal transformations and a and d are vertical. This link provides a more detailed explanation: Transformations

The first and most obvious thing about this transformation was that it was reflected over the x-axis. That can be seen in your function because the leading coefficient ($a$) is negative. Next, your graph has been translated down three units. This is shown in your equation because $d$ is negative 3. Lastly, your graph has been vertically stretched by a factor of 3, since $\left\mid a \right\mid = 3$

Finally, the domain and range. This can be figured out graphically, by looking at the graph and seeing that x must be greater than 0 and y must be less than -3. So, $\left\{x | x \ge 0 , x \in R\right\}$, and $\left\{y | y \le - 3 , y \in R\right\}$.