The function f(x) = x². 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)? (confused more than words can say)

Question

The function  f(x) = x². 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)? (confused more than words can say)

jim_thompson5910 · Answer

Hint: if you translate f(x) using those rules to get g(x), you will get

g(x) = f(x-3) - 3

jim_thompson5910 · Answer

Example: 

f(x) = x^2 + 2x + 5


f(x-3) = (x-3)^2 + 2(x-3) + 5 ... translate 3 units to the right


f(x-3) - 3 = (x-3)^2 + 2(x-3) + 5 - 3 ... translate 3 units down


f(x-3) - 3 = (x-3)^2 + 2(x-3) + 2


So g(x) = (x-3)^2 + 2(x-3) + 2