Question

If the function f(x) = (2x − 3)3 is transformed to g(x) = (-2x − 3)3, which type of transformation occurred?

a.vertical reflection

b.vertical shift

c.vertical shift

d.horizontal shift

Answer 1

Horizontal reflection

Explanation:

original function:
`f(x)=(2x-3)^3`

transformed function:
`g(x)=(-2x-3)^3`

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

`f(x) = (2x - 3)^3\\f(-x)=(2(-x)-3)^3\\f(-x)=(-2x-3)^3\\f(-x)=g(x)`

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).