Question

graph the polynomial function f(x)=x^3 - 4x. 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

The polynomial function is \(f(x)=x^{3}-4x\). The leading - term is the term with the highest power of \(x\), which is \(x^{3}\).

Step2: Determine end - behavior based on the leading - term

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

Answer:

\(x^{3}\)