Question:
In the following graph of [tex]f(x)=-\frac{2}{3} (x-3)^2+2[/tex] 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 [tex]g(x)=-\frac{2}{3} (x+1)^2+1[/tex]
Explanation:
The function is [tex]f(x)=-\frac{2}{3} (x-3)^2+2[/tex]
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
[tex]g(x)=-\frac{2}{3} (x-3+4)^2+2-1[/tex]
Simplifying, we have,
[tex]g(x)=-\frac{2}{3} (x+1)^2+1[/tex]
Hence, the function g(x) is [tex]g(x)=-\frac{2}{3} (x+1)^2+1[/tex]
