​Consider the function $f(x)=x^3−3x−2$.  

1. Rewrite the equation in factored form.

   Hint (a):

   Notice that this is a cubic function. In this case, the roots will be factors of $2$. Use polynomial division to identify the roots and write the equation in factored form.

2. Sketch a graph of the function and describe the end behavior.

   Hint (b):

   Sketch a prediction of the graph and then use a graphing calculator to check the accuracy of your sketch. Be sure to identify and correct any mistakes.

3. Use the graph to locate all the vertical asymptotes of $y=\frac{1}{f(x)}$.

   Hint (c):

   Recall that when $f(x)=0$, $\frac{1}{f\left(x\right)}$ is undefined, so the graph will have a vertical asymptote.