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)?5GOD = x2FO= ?O A. F(x) = -3(x+3)2 + 3O B. F(x) = 3(x - 3)2 - 3O c. F(x) = 3(x + 3)2 + 3D. F(x) = -3(x-3)2 + 3

Answer 1

First, consider that a trasnlation of a function f(x), a units to the left, is represented by the function f(x + a). Moreover, take into account that a vertical translation of a function cosists in adding a constant in the form f(x) + b, where b is the constant.

Then, for the function G(x) = x², you can notice that the function has been traslated to the left 3 units, furthermore, the function concavity opens downward (which means that the dominant coefficient is negative) and there is a vertical translation of 3 units. These operations can be written as follow:

F(x) = -3(x + 3)² + 3