Question: Find the following for the function \(\mathrm{f}(\mathrm{x})=\mathrm{x}^{2}(\mathrm{x}-3)(\mathrm{x}+3)\).

1. Find the \(\mathrm{x}\) - and \(\mathrm{y}\) -intercepts of the polynomial function \(\mathrm{f}\).
2. Determine whether the graph of f crosses or touches the \(\mathrm{x}\) -axis at each \(\mathrm{x}\) -intercept.
3. Find the power function that the graph of \(\mathrm{f}\) resembles for large values of \(|\mathrm{x}|\).
4. Determine the maximum number of turning points on the graph of \(\mathrm{f}\).
5. Determine the behavior of the graph of f near each \(\mathrm{x}\) -intercept.
6. Put all the information together to obtain the graph of \(\mathrm{f}\).

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