Sketching Polynomial Functions

We are given the following function. $$\begin{array}{r}f(x)=x^3+3x^2-4x\end{array}$$ As we can see, the degree of the polynomial is $3.$ It's an odd number, so the ends of the function will go in opposite directions. Hence, the possible answers are I and II. The leading coefficient of the polynomial is $1.$ It is a positive number, which tells us the following. $$\begin{array}{c}\text{As }x\to \text{-}\infty ,f(x)\to \text{-}\infty \\ \text{As }x\to \infty ,f(x)\to \infty \end{array}$$ This means that the function enters the coordinate system from the bottom and exits the top. The only graph that meets all the requirements is II.