Question

The graph of F(x), shown below, resembles the graph of G(X) = x?, but it hasbeen stretched somewhat and shifted. Which of the following could be theequation of F(x)?GOO = x2vi+++-5At5-6FO = ?A. F(x) = -(x-4)2-3O B. F(X) = (x + 4)2 - 3O C. F(x) =x-4)2-3D. F(x) = -(x + 4)2-3

Answer 1

Given the function,

$G(x)=x^2$

The transformation of the function is illustrated below,

Step 1) The image is reflected about the x-axis.

$f(x)=-x^2$

Step 2) The function is shifted down by 3 units.

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

Step 3) It was shifted to the right by 4 units,

$f(x)=-(x-4)^2-3$

Hence, Option A is the correct answer.