Question

1. $f(x) = x^3 + 4x^2 - 3$

$limlimits_{x \to -\infty} f(x) = -\infty$
$limlimits_{x \to \infty} f(x) = \infty$

Explanation:

Step1: Identify dominant term

For polynomial $f(x)=x^3+4x^2-3$, the highest-degree term $x^3$ dictates end behavior.

Step2: Evaluate limit as $x\to-\infty$

As $x\to-\infty$, $x^3\to-\infty$; lower terms become negligible.
$\lim_{x\to-\infty} (x^3+4x^2-3) = -\infty$

Step3: Evaluate limit as $x\to\infty$

As $x\to\infty$, $x^3\to\infty$; lower terms become negligible.
$\lim_{x\to\infty} (x^3+4x^2-3) = \infty$

Answer:

$\lim_{x\to-\infty} f(x) = -\infty$
$\lim_{x\to\infty} f(x) = \infty$