Answer:
Horizontal reflection
Step-by-step explanation:
original function: [tex]f(x)=(2x-3)^3[/tex]
transformed function: [tex]g(x)=(-2x-3)^3[/tex]
if you have a function f(x), when you do a horizontal reflection the function must become f(-x). so in this case we must see if g(x) = f(-x) to confirm is the transformation is a horizontal reflection:
f(-x) means that in the original function f(x) where we have x we are going to substitute -x
[tex]f(x) = (2x - 3)^3\\f(-x)=(2(-x)-3)^3\\f(-x)=(-2x-3)^3\\f(-x)=g(x)[/tex]
Thus we check that the condition for horizontal reflection is met.
Another way to check this is to graph both functions on some page or mathematical software and check that g(x) is a horizontal reflection of f(x), it is as if the y axis were a mirror (see attached image).
