Question

graph the polynomial function f(x)=x^3 + x^2 - 6x. answer parts (a) through (e). (a) determine the end behavior of the graph of the function. the graph of f behaves like y = for large values of |x|.

Explanation:

Step1: Identify the leading - term

For the polynomial function \(f(x)=x^{3}+x^{2}-6x\), the leading - term is the term with the highest power of \(x\). Here, the leading - term is \(x^{3}\).

Step2: Determine end - behavior

For a polynomial function \(y = a_nx^n+\cdots+a_0\) (\(a_n
eq0\)), when \(n\) is odd and \(a_n>0\) (in \(y = x^{3}\), \(n = 3\) (odd) and \(a_n = 1>0\)), as \(x\to+\infty\), \(y\to+\infty\) and as \(x\to-\infty\), \(y\to-\infty\). The end - behavior of the graph of \(y = f(x)\) is determined by the leading - term. So, for large values of \(|x|\), the graph of \(f\) behaves like \(y=x^{3}\).

Answer:

\(x^{3}\)