Answer: Reflection across the x-axis.
Step-by-step explanation:
The correct exercise is: The correct exercise is: "If the parent function[tex]f(x) = (2x - 3)^3[/tex] is transformed to [tex]g(x) = (-2x + 3)^3[/tex] , which type of transformation occurs?
"
There are several transformations for a function f(x). Two of those transformations are shown below:
1. If [tex]-f(x)[/tex], then the function is reflected across the x-axis.
2. If [tex]f(-x)[/tex], then the function is reflected across the y-axis.
In this case, the exercise provides you the following function f(x):
[tex]f(x) = (2x - 3)^3[/tex]
And you know that the function g(x) is obtained by transforming the function f(x). The function g(x) is:
[tex]g(x) = (-2x + 3)^3[/tex]
Which can written as:
[tex]g(x) = -(2x - 3)^3[/tex]
Therefore, you can identify (based on the transformations shown at the beginning of the explanation), that:
[tex]g(x)= -f(x)[/tex]
Therefore, the function [tex]g(x) = (-2x + 3)^3[/tex] is obtained by reflecting the function [tex]f(x) = (2x - 3)^3[/tex] across the x-axis.
