1. The problem involves understanding and analyzing polynomial functions, which are expressions involving variables raised to whole number powers combined by addition, subtraction, and multiplication. 2. A general polynomial function looks like $$y = a_nx^n + a_{n-1}x^{n-1} + \cdots + a_1x + a_0,$$ where $a_n, a_{n-1}, \ldots, a_0$ are constants and $n$ is a non-negative integer. 3. To graph a polynomial function, identify important features such as intercepts and extrema (minimum and maximum points). 4. The $x$-intercepts are the solutions of the polynomial equation $y=0$ and can be found by factoring or using numerical methods. 5. Extrema are points where the slope of the polynomial is zero and can be found by taking the derivative and solving $y' = 0$. 6. Understanding the degree $n$ of the polynomial helps determine the general shape and number of extrema. 7. The leading coefficient $a_n$ indicates the end behavior of the polynomial graph. 8. Plotting these features gives a clear visual insight into the polynomial's characteristics.