The function f(x) =x^2. The graph of g (x) is f (x) translated to the right 3 units and down 3 units. What is the function rule for g(x)

Question

I am needing help with the following question I know how to get the answer by looking at an example but I need help with finding it for myself.

Answer 1

f(x)=x^2

when you translate to the right, you subtract, and when you translate to the left, you add; it's the opposite of what you would expect

when you translate down, you subtract and when you translate up you add, just what you would expect

g(x)=(x-3)^2-3

to help you understand the "-3", compare y=x^2 and y=(x-3)^2

if x=1, then y=1 in the first function

to get the same y-value, 1, in the second function, x must equal 4 (or 2)

if you had y=(x+3)^2, then x would have to be -4 which means the function is translated to the left, not the right as specified