select the correct answer. which pair of statements describes the end - behavior of the graph of the…

select the correct answer. which pair of statements describes the end - behavior of the graph of the function f(x)=x³ + 2x² - 5x - 6? a. as x approaches negative infinity, f(x) approaches infinity. as x approaches infinity, f(x) approaches infinity. b. as x approaches negative infinity, f(x) approaches infinity. as x approaches infinity, f(x) approaches negative infinity. c. as x approaches negative infinity, f(x) approaches negative infinity. as x approaches infinity, f(x) approaches negative infinity. d. as x approaches negative infinity, f(x) approaches negative infinity. as x approaches infinity, f(x) approaches infinity.

select the correct answer. which pair of statements describes the end - behavior of the graph of the function f(x)=x³ + 2x² - 5x - 6? a. as x approaches negative infinity, f(x) approaches infinity. as x approaches infinity, f(x) approaches infinity. b. as x approaches negative infinity, f(x) approaches infinity. as x approaches infinity, f(x) approaches negative infinity. c. as x approaches negative infinity, f(x) approaches negative infinity. as x approaches infinity, f(x) approaches negative infinity. d. as x approaches negative infinity, f(x) approaches negative infinity. as x approaches infinity, f(x) approaches infinity.

Answer

Explanation:

Step1: Identify the degree and leading - coefficient

The function $f(x)=x^{3}+2x^{2}-5x - 6$ is a cubic function (degree $n = 3$, which is odd) and the leading - coefficient $a = 1$ (positive).

Step2: Determine the end - behavior rules

For a polynomial function $y = a x^{n}+b x^{n - 1}+\cdots+z$ with odd degree $n$ and positive leading - coefficient $a$: when $x\to-\infty$, $y\to-\infty$; when $x\to\infty$, $y\to\infty$.

Answer:

D. As x approaches negative infinity, f(x) approaches negative infinity. As x approaches infinity, f(x) approaches infinity.