Answer:
A. horizontal reflection
Step-by-step explanation:
Given:
[tex]f(x)=(2x-3)^2[/tex]
[tex]g(x)=(-2x-3)^2[/tex]
To identify the type of transformation.
Solution:
On close observation of the functions we find the that sign of [tex]x[/tex] has changed in [tex]g(x)[/tex] with other terms being constant.
Thus, the transformation statement can be given as:
[tex]f(x)\rightarrow f(-x)[/tex]
As:
[tex]f(x)=(2x-3)^2[/tex]
[tex]f(-x)=(2(-x)-3)^2= (-2x-3)^2 = g(x)[/tex]
The transformation [tex]f(x)\rightarrow f(-x)[/tex] describes horizontal reflection of function across the y-axis.
Thus, [tex]f(x)[/tex] is horizontally reflected across y-axis to get [tex]g(x)[/tex].
