The function \( g \) is defined as follows. \( g(x)=-2 x^{2}-4 \) If the graph of \( g \) is translated vertically downward by 5 units, it becomes the graph of a function \( f \). Find the expression for \( f(x) \). Note that the ALEKS graphing calculator may be helpful in checking your answer. \( f(x)=\square \)

To find the expression for \( f(x) \), we start with the original function \( g(x) = -2x^{2} - 4 \) and perform a vertical translation downward by 5 units. This means we will subtract 5 from the entire function \( g(x) \). So, we have: \[ f(x) = g(x) - 5 \] Substituting \( g(x) \): \[ f(x) = (-2x^{2} - 4) - 5 \] Simplifying this gives us: \[ f(x) = -2x^{2} - 4 - 5 = -2x^{2} - 9 \] Thus, the expression for \( f(x) \) is: \[ f(x) = -2x^{2} - 9 \]