Question

the function $f(x)$ is defined below. what is the end behavior of $f(x)$?
$f(x) = 9x^3 - 18x^2 - 279x - 252$
answer
as $x \to -\infty, y \to \infty$ and
as $x \to \infty, y \to \infty$
as $x \to -\infty, y \to -\infty$ and
as $x \to \infty, y \to -\infty$
as $x \to -\infty, y \to \infty$ and
as $x \to \infty, y \to -\infty$
as $x \to -\infty, y \to -\infty$ and
as $x \to \infty, y \to \infty$

Explanation:

Step1: Identify degree and leading coefficient

The function is $f(x)=9x^3 - 18x^2 - 279x - 252$. Degree $n=3$ (odd), leading coefficient $a=9$ (positive).

Step2: Apply end behavior rules

For odd degree, positive leading coefficient:

• As $x \to -\infty$, $f(x) \to -\infty$
• As $x \to \infty$, $f(x) \to \infty$

Answer:

as $x \to -\infty, y \to -\infty$ and as $x \to \infty, y \to \infty$