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

Explanation:

Step1: Horizontal translation right 4 units

For a function $f(x)$, shifting right by $h$ units gives $f(x-h)$. Here $h=4$, so $f(x-4)=(x-4)^2$.

Step2: Vertical translation up 9 units

Shifting a function up by $k$ units adds $k$ to the function. Here $k=9$, so $g(x)=(x-4)^2 + 9$.

Answer:

g(x) = (x - 4)² + 9