Question

the function ( f(x) = x^2 ) has been translated 9 units up and 4 units to the right to form the function ( g(x) ). which represents ( g(x) )?
( circ g(x) = (x + 9)^2 + 4 )
( circ g(x) = (x + 9)^2 - 4 )
( circ g(x) = (x - 4)^2 + 9 )
( circ g(x) = (x + 4)^2 + 9 )

Explanation:

Step1: Horizontal translation rule

For right shift by $h$: $f(x) \to f(x-h)$
Here, $h=4$, so $x^2 \to (x-4)^2$

Step2: Vertical translation rule

For up shift by $k$: $f(x) \to f(x)+k$
Here, $k=9$, so $(x-4)^2 \to (x-4)^2 + 9$

Answer:

C. $g(x) = (x - 4)^2 + 9$