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Answer:
Step-by-step explanation:
Here we can see that the parent function is 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
Where as
{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
The ratio between the surfaces areas of the two prisms is equal to 6.25.
<h3>How to get the ratio of the surface areas?</h3>
The ratio between the volumes of the prisms is:
This number is equal to the cube of the scale of dilation applied to the dimensions of the smaller prism, so the scale factor is:
And the ratio between the areas should be the square of the scale factor, then we will have that the ratio between the surface areas of the two prisms is:
If you want to learn more about scale factors, you can read: