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)?

Answer 1

Answer:

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

Step-by-step explanation:

It is given that f(x) is $x^{2}$.

The graph is basically a parabola opening upward with vertex at origin.If we shift it right by 3 units and down by 3 units, the graph will still be a parabola opening upward but with vertex (3,-3).

The general equation of a parabola opening upward with vertex (a,b) is given by:

y-b = $(x-a)^{2}$

In this case a=3 and b=-3, then we get

y = $(x-3)^{2}-3$ = $x^{2}-6x+6$

Hence g(x) becomes $x^{2}-6x+6$.