Answer:
[tex]g(x)= \frac{1}{9} \times x^2[/tex]
Step-by-step explanation:
Here we can see that the parent function is [tex]f(x)=x^2[/tex] and the translated function is g(x). f(x) is a parabola.
Rule says that any factor if multiplied by f(x) is going to contract the graph towards the y axis and vice versa.
Similarly any factor if f(x) is divided by some factor it is going to be stretch the graph away from the y axis and vice versa.
Here we can see that the translated graph g(x) is stretched away from the y axis with reference to the parent function f(x). Hence as per he rule discussed above, we get a preliminary information that the parent function f(x) is being divided by some factor.
now we are given that
[tex]f(x) = x^2[/tex]
[tex]f(3) = 3^2 = 9[/tex]
Where as
[tex]g(3) = 1[/tex] {as given in the graph}
Hence
at x=3 , f(x) = 9 and g(x) = 1 , and also we have discussed above that f(x) is divided by some factor. Hence [tex]g(x)= \frac{1}{9}f(x)[/tex]
[tex]g(x)= \frac{1}{9} \times x^2[/tex]
