Function f(x) undergoes a simple transformation to create function g(x).

the graphs of both f(x) and g(x) are shown.

create g(x) in terms of f(x).

Are there choices? The answer without choices 

g(x) = f(x) + 3

Find the value of a 

It could be f(x) = a(x - 1)^2 so you have to check out the value of a

f(x) = y = a(x - 1)^2 Let x = 3

f(x) = y = a(3 -1)^2

4 = 2^2 * a The 4 comes from the graph. Follow 3 up until it hits f(x) then read across on the y axis.

a = 2^2 / 4

a = 1

Conclusion

f(x) = a(x - 1)^2

f(x) = (x - 1)^2

find g(x) 

Just looking at the bottom point (the minimum of f(x) and g(x) ) you see that  g(x) is 3 units above f(x)

So g(x) = (x - 1)^2 + 3 

So g(x) = f(x) + 3 <<<<<<<< answer.

If there are choices, please list them. I am changing this at the request of a mod. Without choices, I believe either answer to be correct.

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step-by-step explanation: