Write an equation for the function whose graph is described. the shape of \( f(x)=x^{3} \), but shifted seven units to the left, three units down, and then reflected in the \( y \)-axis \( g(x)=\square \)

We start with the basic function \[ f(x) = x^3. \] 1. Shift seven units to the left by replacing \(x\) with \(x+7\): \[ f(x+7) = (x+7)^3. \] 2. Shift three units down by subtracting 3 from the function: \[ (x+7)^3 - 3. \] 3. Reflect in the \(y\)-axis by replacing \(x\) with \(-x\): \[ \left((-x)+7\right)^3 - 3 = (7 - x)^3 - 3. \] Thus, the function is \[ g(x) = (7 - x)^3 - 3. \]