the function f(x) = x² has been translated 9 units up and 4 units to the right to form the function g(x)…

the function f(x) = x² has been translated 9 units up and 4 units to the right to form the function g(x). which represents g(x)?\n○ g(x)=(x + 9)²+4\n○ g(x)=(x + 9)² - 4\n○ g(x)=(x - 4)²+9\n○ g(x)=(x + 4)²+9

the function f(x) = x² has been translated 9 units up and 4 units to the right to form the function g(x). which represents g(x)?\n○ g(x)=(x + 9)²+4\n○ g(x)=(x + 9)² - 4\n○ g(x)=(x - 4)²+9\n○ g(x)=(x + 4)²+9

Answer

Explanation:

Step1: Recall horizontal - translation rule

For a function $y = f(x)$, a translation of $h$ units to the right gives $y=f(x - h)$. Here, $h = 4$, so $f(x)$ becomes $f(x - 4)=(x - 4)^2$.

Step2: Recall vertical - translation rule

For a function $y = f(x)$, a translation of $k$ units up gives $y=f(x)+k$. Here, $k = 9$. So, after the horizontal translation, when we translate 9 units up, the function becomes $g(x)=(x - 4)^2+9$.

Answer:

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