Use the following information to answer the next question The graph of $f(x)=x^{2}$ is transformed with the following transformations: - reflection in the $x$-axis - vertically stretched about the $x$-axis by a factor of 3 - translated 8 units to the left and 1 unit down 2. The resulting function, $g(x)$ is $g(x)=-3(x+8)^{2}-1$ $g(x)=-3(x-8)^{2}-1$ $g(x)=3(x-8)^{2}-1$ $g(x)=3(x+8)^{2}-1$

Step 1 ：The question is asking for the resulting function after applying the transformations to the function \(f(x)=x^{2}\).

Step 2 ：The transformations are: reflection in the x-axis, vertically stretched about the x-axis by a factor of 3, translated 8 units to the left and 1 unit down.

Step 3 ：Reflection in the x-axis changes the sign of the function, so \(f(x)\) becomes \(-f(x)\).

Step 4 ：Vertically stretching about the x-axis by a factor of 3 multiplies the function by 3, so \(-f(x)\) becomes \(-3f(x)\).

Step 5 ：Translating 8 units to the left and 1 unit down changes \(x\) to \(x+8\) and subtracts 1 from the function, so \(-3f(x)\) becomes \(-3f(x+8)-1\).

Step 6 ：Substituting \(f(x)=x^{2}\) into the transformed function gives \(g(x)=-3(x+8)^{2}-1\).

Step 7 ：Final Answer: The resulting function, \(g(x)\) is \(\boxed{g(x)=-3(x+8)^{2}-1}\).