The graph of the parent function [tex]y = \sqrt{x}[/tex] is transformed when graphing[tex]y = -3\sqrt{x-6}[/tex] and this can be done by translating the graph by 6 units in the positive x-axis and then taking the image about the x-axis.
Given :
- Parent Function - [tex]y = \sqrt{x}[/tex]
- Transformed Function - [tex]y = -3\sqrt{x-6}[/tex]
The following steps can be used to transform the graph of [tex]y = \sqrt{x}[/tex] in [tex]y = -3\sqrt{x-6}[/tex] :
Step 1 - First draw the graph of [tex]y = \sqrt{x}[/tex].
Step 2 - Now, translate the graph of [tex]y = \sqrt{x}[/tex] in positive x-direction by 6 units. The resulting graph is the graph of [tex]y = \sqrt{x-6}[/tex].
Step 3 - Now, multiply the y-axis by a factor of 3. The resulting graph is the graph of [tex]y = 3\sqrt{x-6}[/tex].
Step 4 - Take the image of the graph obtained in the above step about the x-axis. The resulting graph is the graph of [tex]y = -3\sqrt{x-6}[/tex].
For more information, refer to the link given below:
https://brainly.com/question/10712002
