Question

the function $f(x)$ is defined below. what is the end behavior of $f(x)$?
$f(x) = -132x + 6x^3 - 144 + 18x^2$
answer
$\circ$ as $x \to \infty, f(x) \to \infty$ and as $x \to -\infty, f(x) \to \infty$
$\circ$ as $x \to \infty, f(x) \to \infty$ and as $x \to -\infty, f(x) \to -\infty$
$\circ$ as $x \to \infty, f(x) \to -\infty$ and as $x \to -\infty, f(x) \to \infty$
$\circ$ as $x \to \infty, f(x) \to -\infty$ and as $x \to -\infty, f(x) \to -\infty$

Explanation:

Step1: Rearrange to standard form

$f(x) = 6x^3 + 18x^2 - 132x - 144$

Step2: Identify leading term

Leading term: $6x^3$

Step3: Analyze degree and coefficient

Degree = 3 (odd), leading coefficient = 6 (positive)

Step4: Determine end behavior

For odd degree, positive leading coefficient:
As $x \to \infty$, $f(x) \to \infty$; as $x \to -\infty$, $f(x) \to -\infty$

Answer:

as $x \to \infty, f(x) \to \infty$ and as $x \to -\infty, f(x) \to -\infty$