Question

In the following graph of F(x) = -(2/3)(x-3)2 + 2 is the preimage of a transformation of G(x)which is the image. What is the mapping statement for the function G(x)?

Answer 1

Question:

In the following graph of $f(x)=-\frac{2}{3} (x-3)^2+2$ is the preimage of a transformation of G(x)which is the image. What is the mapping statement for the function G(x)?

The image of the transformed graph is attached below:

Answer:

The function g(x) is $g(x)=-\frac{2}{3} (x+1)^2+1$

Explanation:

The function is $f(x)=-\frac{2}{3} (x-3)^2+2$

Let us determine the transformed equation of the function from the graph.

From the graph, we can see that the function g(x) is shifted 1 unit downwards and shifted 4 units to the left.

Thus, the function g(x) can be written as

$g(x)=-\frac{2}{3} (x-3+4)^2+2-1$

Simplifying, we have,

$g(x)=-\frac{2}{3} (x+1)^2+1$

Hence, the function g(x) is $g(x)=-\frac{2}{3} (x+1)^2+1$