We want to get g(x) given that we know f(x) and the graphs for both functions. We will see that the correct option is D:
g(x) = (x/3)^2
By looking at the graph we can see that f(x) and g(x) are two quadratic functions, and g(x) is just a dilation of f(x).
This means that:
g(x) = A*f(x)
Where A is a real number.
We know that:
f(x) = x^2
And by looking at the graph, we also know that g(3) = 1.
Then we can write:
g(3) = A*f(3) = A*3^2 = 1
Now we can solve this for A:
A*3^2 = 1
A*9 = 1
A = 1/9
Then we have:
g(x) = (1/9)*f(x) = (1/9)*x^2 = (x/3)^2
So the correct option is D.
If you want to learn more about quadratic equations, you can read:
https://brainly.com/question/1214333
