Question

consider the end behaviors of $f(x) = x^4 - 3x^2 - 4$. move the values into the table to show the end behaviors of the graph of $f(x)$. \\(x \to -\infty, f(x) \to\\) \\(x \to +\infty, f(x) \to\\) values: $1$, $-3$, $-4$, $+\infty$

Explanation:

Step1: Identify leading term

The leading term of $f(x)=x^4 - 3x^2 - 4$ is $x^4$.

Step2: Analyze degree and leading coefficient

Degree is 4 (even), leading coefficient is 1 (positive). For even degree with positive leading coefficient: as $x\to\pm\infty$, the leading term dominates, so $x^4\to+\infty$.

Step3: Evaluate end behavior

When $x\to -\infty$, $f(x)\to+\infty$; when $x\to +\infty$, $f(x)\to+\infty$.

Answer:

End Behavior	Value
$x\to +\infty, f(x)\to$	$+\infty$