Question

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)?

Please Help!!

Answer 1

`g(x)=x^2-6x+6`

Explanation:

Translation of a function

The original function f is

`f(x)=x^2`

We need to define a second function such as its graph is translated 3 units to the right and 3 units below f(x)

The new function called g(x) must be translated horizontally and vertically. To have it translated to the right, we must replace x by x-3 and to translate the result down, we must subtract 3 as shown

`g(x)=f(x-3)-3`

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

`g(x)=x^2-6x+9-3`

`g(x)=x^2-6x+6`

Both graphs are shown in the figure below where we can see the translation in both axes