the function $f(x)=x^{2}$ is translated 7 units to the left and 3 units down to form the function $g(x)$…

the function $f(x)=x^{2}$ is translated 7 units to the left and 3 units down to form the function $g(x)$. which represents $g(x)$?\n$g(x)=(x - 7)^{2}-3$\n$g(x)=(x + 7)^{2}-3$\n$g(x)=(x - 3)^{2}-7$\n$g(x)=(x - 3)^{2}+7$

the function $f(x)=x^{2}$ is translated 7 units to the left and 3 units down to form the function $g(x)$. which represents $g(x)$?\n$g(x)=(x - 7)^{2}-3$\n$g(x)=(x + 7)^{2}-3$\n$g(x)=(x - 3)^{2}-7$\n$g(x)=(x - 3)^{2}+7$

Answer

Answer:

B. $g(x)=(x + 7)^2-3$

Explanation:

Step1: Recall horizontal - translation rule

For a function $y = f(x)$, translating it $h$ units to the left gives $y=f(x + h)$. Here $h = 7$, so $f(x)=x^2$ becomes $y=(x + 7)^2$.

Step2: Recall vertical - translation rule

For a function $y = f(x)$, translating it $k$ units down gives $y=f(x)-k$. Here $k = 3$, so $(x + 7)^2$ becomes $g(x)=(x + 7)^2-3$.