\begin{tabular}{l} Section 3.4 \#54 Find the degree, end \\ behavior, x- and y-intercepts, zeroes of \\ multiplicity, and a few midinterval \\ points of the function. You do not \\ need to graph the function. \\ \hline\end{tabular}

Let’s dive into some fun facts about polynomial functions! They are often seen as the superheroes of mathematics, capable of modeling various real-world phenomena, from the trajectory of a basketball to the behavior of stock prices. Polynomials can have different degrees, which dictate how many times they can cross the x-axis (i.e., their zeroes) and their overall end behavior, which basically describes whether they rise or fall towards infinity. Now, when tackling problems like the one you're working on, it’s essential to remember a few common pitfalls. One classic mistake is neglecting to check the multiplicity of zeroes, as zeroes of even multiplicity will "touch" the x-axis and not cross it. Additionally, when determining intercepts, always ensure to evaluate your function correctly, as miscalculating an intercept might lead to an entirely wrong interpretation of the function's behavior! Stay sharp and keep practicing!