Answer:
Option D - It is horizontally compressed by a factor of 2 and reflected over the y-axis.
Step-by-step explanation:
Given : The graph of [tex]y=\sqrt{-2x}[/tex] related to its parent function [tex]y=\sqrt{x}[/tex].
To find : How is the graph translated?
Solution :
Let,
The parent function [tex]f(x)=\sqrt{x}[/tex]
Translated function [tex]g(x)=\sqrt{-2x}[/tex]
- In the parent function, the graph is reflected over y-axis as
The reflection of the point (x,y) across the y-axis is the point (-x,y).
f(x,y)→f(-x,y)
[tex]g(x)=\sqrt{-x}[/tex]
- In the parent function, the graph is horizontally compressed as
The compression horizontally the function became
y=f(x)→ y=f(bx) , b is the compression factor and b>1
[tex]y=\sqrt{x}[/tex] → [tex]y=\sqrt{-2x}[/tex] , function is compressed by 2 unit.
Therefore, Option D is correct.
It is horizontally compressed by a factor of 2 and reflected over the y-axis.
We plot the graph of both the equations in which translation is shown.
Refer the attached graph below.
