Question

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

Answer 1

Answer:

A. horizontal reflection

Step-by-step explanation:

Given:

$f(x)=(2x-3)^2$

$g(x)=(-2x-3)^2$

To identify the type of transformation.

Solution:

On close observation of the functions we find the that sign of $x$ has changed in $g(x)$ with other terms being constant.

Thus, the transformation statement can be given as:

$f(x)\rightarrow f(-x)$

As:

$f(x)=(2x-3)^2$

$f(-x)=(2(-x)-3)^2= (-2x-3)^2 = g(x)$

The transformation $f(x)\rightarrow f(-x)$ describes horizontal reflection of function across the y-axis.

Thus, $f(x)$  is horizontally reflected across y-axis to get $g(x)$.