f(x) = (2x - 3)³
g(x) = -(2x - 3)³ this is a reflection across the x-axis
The type of transformation is the reflection across the x-axis.
We are given a parent function f(x) by:
[tex]f(x)=(2x-3)^3[/tex]
and the transformed function g(x) is given by:
[tex]g(x)=(-2x+3)^3[/tex]
which could also be written as:
[tex]g(x)=(-(2x-3))^3\\\\i.e.\\\\g(x)=(-1)^3\cdot (2x-3)^3\\\\i.e.\\\\g(x)=-(2x-3)^3\\\\i.e.\\\\g(x)=-f(x)[/tex]
i.e. the transformation g(x) is obtained by reflecting the parent function f(x) across the x-axis.
( Since, when the reflection of a function is done across the x-axis then the x-coordinate of the point of the function remains the same and the y-coordinate of the point takes the negative sign.
i.e. f(x) → -f(x)
i.e.
(x,y) → (x,-y) )
