Answer
See graph.
Work Step by Step
Step 1. Given $f(x)=x^4+x^3-3x^2-4x-4=(x+2)(x-2)(x^2+x+1)$, we can find its zeros as $x=\pm2$, y-intercept $f(0)=-4$. Function is neither even nor odd. End behavior: rise to the right and rise to the left. Maximum number of turning points $3$.
Step 2. Use the information above and test points to graph the function as shown in the figure.