\( 1 \leftarrow \) Analyze the polynomial function \( f(x)=x^{2}(x-3) \) using parts (a) through (e). (a) Determine the end behavior of the graph of the function. The graph of \( f \) behaves like \( y=\square \) for large values of \( |x| \).

The end behavior of the graph of the function \( f(x) = x^{2}(x-3) \) can be analyzed by focusing on the leading term as \( x \) approaches positive or negative infinity. Since the highest degree term is \( x^{3} \), the graph behaves like \( y = x^{3} \) for large values of \( |x| \). This means that as \( x \to \infty \), \( f(x) \to \infty \), and as \( x \to -\infty \), \( f(x) \to -\infty \). To visualize this better, remember that polynomial functions are smooth and continuous. The degree of this polynomial (3) also indicates that it will have one end going to infinity and the other end going to negative infinity. This makes for interesting curves that can cross the x-axis at various points, depending on the factors present in the polynomial!