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

1 Answer
Feb 4, 2018

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


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}#.