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

Explanation:

Step1: Recall horizontal translation rule

For a right shift by $h$ units: $f(x) \to f(x-h)$

Step2: Apply horizontal shift to $f(x)$

$f(x) = x^2$ shifted 4 right: $(x-4)^2$

Step3: Recall vertical translation rule

For an upward shift by $k$ units: $f(x) \to f(x)+k$

Step4: Apply vertical shift to the result

$(x-4)^2$ shifted 9 up: $(x-4)^2 + 9$

Answer:

$g(x)=(x - 4)^2 + 9$ (Option 3)