Question

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

Answer 1

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

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*sqrt(b(x+c))+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 `abs(a) = 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, `{x | x ge 0, x in R}`, and `{y | y le -3, y in R}`.