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

Answer:

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

Step-by-step 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