Write a formula for the function, $g(x)$, described as follows: Use the function, $f(x)=\sqrt[3]{x}$. Move the function to the left by 4 units and down by 3 units. Answer \[ g(x)= \]

Step 1 ：The question is asking for a transformation of the function \(f(x)=\sqrt[3]{x}\). Moving the function to the left by 4 units means replacing \(x\) with \((x+4)\) in the function. Moving the function down by 3 units means subtracting 3 from the function. So, the transformed function, \(g(x)\), should be \(\sqrt[3]{x+4}-3\).

Step 2 ：Final Answer: \(g(x)=\boxed{\sqrt[3]{x+4}-3}\)