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

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 $y=(x + 7)^{2}$ after translating 7 units to the left.

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 the function after translating 3 units down from $y=(x + 7)^{2}$ is $y=(x + 7)^{2}-3$.

Answer:

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