1. The problem asks if Stephanie's argument about restricting the domain of the function $f(x) = (x - 4)^3$ to ensure its inverse $f^{-1}(x) = \sqrt[3]{x} + 4$ is a function is correct. 2. The function $f(x) = (x - 4)^3$ is a cubic function, which is one-to-one and passes the horizontal line test over all real numbers. This means it already has an inverse function without any domain restriction. 3. The inverse function $f^{-1}(x) = \sqrt[3]{x} + 4$ is defined for all real $x$ because cube roots are defined for all real numbers. 4. Stephanie claims the domain must be restricted to $x \geq 4$ to graph only the "top half" of $f^{-1}$, but this is unnecessary because the original function is one-to-one on $(-\infty, \infty)$. 5. Therefore, the correct conclusion is that Stephanie's argument is incorrect because no domain restriction is needed for $f$ to have an inverse function. 6. This matches option C: "YES, $f$ is a cubic function that passes the horizontal line test, so she did not need to restrict the domain."