Question

answer parts (a)-(e) for the function shown below. f(x)=x^3 + 2x^2 - x - 2 a. use the leading - coefficient test to determine the graphs end behavior. which statement describes the behavior at the ends of f(x)=x^3 + 2x^2 - x - 2? a. the graph falls to the left and rises to the right. b. the graph rises to the left and falls to the right. c. the graph falls to the left and to the right. d. the graph rises to the left and to the right.

Explanation:

Step1: Identify the degree and leading - coefficient

The function is \(f(x)=x^{3}+2x^{2}-x - 2\), which is a cubic function (\(n = 3\)) with a leading - coefficient \(a = 1\).

Step2: Apply the leading - coefficient test

For a polynomial function \(y = a_nx^n+\cdots+a_0\), when \(n\) is odd and \(a_n>0\), as \(x\to-\infty\), \(y\to-\infty\) (the graph falls to the left), and as \(x\to+\infty\), \(y\to+\infty\) (the graph rises to the right).

Answer:

A. The graph falls to the left and rises to the right.