Let $f(x)=x^4−4x^3−6x^2+20x−75$.  

1. Identify all of the roots of the function.

   Hint (a):

   All of the rational roots will be factors of $75$. You can graph the function to help see the rational roots.
   Recall that if $x=a$, then $(x−a)$ is a factor that can be divided out of the polynomial.

2. Use the roots to sketch a prediction of what you think the graph of $y=f(x)$ will look like.

3. Use a graphing calculator to check your prediction.