the function $f(x)=x^{2}$ has been translated 9 units up and 4 units to the right to form the function…

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 $g(x)$?\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 $f(x)=x^{2}$ 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

Answer:

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

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 $(x - 4)^2$ becomes $(x - 4)^2+9$.